Mass measurements of neutron-deficient nuclei and their implications for astrophysics

During the years 2005-2010 the double-Penning-trap mass spectrometer JYFLTRAP has been used to measure the masses of 90 ground and 8 isomeric states of neutron-deficient nuclides with a typical precision of better than 10keV. The masses of 14 nuclides -- 84Zr , 88, 89Tc , 90-92Ru , 92-94Rh , 94, 95Pd , 106, 108, 110Sb -- have been experimentally determined for the first time. This article gives an overview on these measurements and their impact on the modeling of the astrophysical rp -process.


Introduction
Very neutron-deficient nuclei are synthesized in astrophysical environments, where extreme temperatures and densities as well as an abundance of hydrogen can lead to a rapid proton capture process (rp-process) [1,2]. As proton capture rates become faster than β + decays, unstable neutron-deficient nuclei are built up. The most common occurrences of such a scenario are type-I X-ray bursts, which occur on the surface of neutron stars that accrete hydrogen-rich matter from a companion star in a stellar binary system. The hydrogen-rich fuel layer on the neutron star surface builds up for hours to days before it explodes giving rise to a bright X-ray burst typically lasting for 10-100 seconds. Such bursts are frequently observed with modern X-ray observatories and are directly powered by the nuclear energy generated in the rp-process reaching nuclei up to tellurium [3][4][5].
Recently, a new astrophysical process with rapid proton captures on neutron-deficient nuclei has been proposed, the νp-process [6][7][8]. It takes place in supernovae and possibly in gamma-ray bursts where proton-rich outflows are created by strong neutrino fluxes [6]. In the νpprocess, the flow towards heavier elements is accelerated via fast (n, p) reactions on long-lived nuclides along the path of the rp-process. The neutrons that induce these reactions are created via antineutrino absorptions on protons. It has been shown that the reaction sequence can a e-mail: anu.k.kankainen@jyu.fi reach nuclei up to A = 108 or A = 152 depending on the electron fraction [9].
Nova explosions are a third astrophysical environment where a mild form of the rp-process takes place. They occur when an accreted fuel layer on the surface of a white dwarf star explodes. The rp-process in novae typically proceeds near stability and is predicted to end in the A = 40 region [10][11][12][13], though recent model calculations have identified parameters that can lead to much more violent explosions with a stronger rp-process reaching the iron region [14]. Accurate nuclear physics is needed to predict the contributions of novae and the νp-process to Galactic nucleosynthesis, to interpret X-ray burst light curves in terms of neutron star properties and to predict the composition of the ashes of X-ray bursts needed to model neutron star crusts. With accurate nuclear physics one can also predict new observables that observational programs can search for.
Nuclear masses play a central role in rapid proton capture processes [3,[15][16][17][18][19][20][21]. When proton capture rates are high, it is photodisintegration that limits further proton captures and forces the reaction sequence to proceed via a β + decay or a (n, p) reaction. Such photodisintegration rates depend exponentially on the energy required to remove a proton from the nucleus, and therefore on the nuclear masses. In addition, many of the important proton capture rates in the rp-process are governed by resonances. Rates depend exponentially on resonance energies, which, in most cases, are determined by measuring excitation energies and nuclear masses. Typically, a precision of around 10 keV is required, for some resonant reaction rates even much better than 10 keV [16]. Penning-trap mass measurements have had a major impact on nuclear astrophysics, as they can easily reach or surpass such precision even for the most unstable nuclei within reach. This is illustrated in fig. 1, where Penning-trap mass measurements since the Atomic Mass Evaluation 2003 (AME03) are highlighted. Clearly, the Penning-trap approach has addressed the long-standing problem of unreliable and uncertain experimental masses of unstable nuclei and has been applied to a large number of neutron-deficient nuclei close to or in the rp-process. In some cases, the effort to push to the most exotic nuclei has led to the paradox situation that now some of the masses of exotic isotopes are better known than their more stable counterparts. The program to measure masses of unstable nuclei with JYFLTRAP has been a major contributor to this success together with CPT [22] at ANL, ISOLTRAP [23] at CERN-ISOLDE, LEBIT [24] at NSCL, and SHIPTRAP [25] at GSI. In addition to nuclear astrophysics, neutron-deficient nuclei offer a wealth of other interesting physics phenomena to be studied. For example, Q EC -value measurements at JYFLTRAP have been useful for testing the isobaric multiplet mass equation [26,27] and the Conserved Vector Current (CVC) hypothesis [28]. Masses of neutrondeficient nuclei provide also important data for developing and testing different mass models. Energy systematics, such as two neutron or proton separation energies, yield information, e.g., on the possible onset of deformation and the evolution of shell-gap energies as well as on neutronproton pairing and the Wigner energy [29].

Experimental methods
The ions of interest have been produced with beams from the K-130 cyclotron of the JYFL Accelerator Laboratory impinging on a thin (few mg/cm 2 ) target situated at the Ion-Guide Isotope Separator On-Line (IGISOL) facility [30]. Which ion guide is used depends on the applied beam: a heavy primary beam would cause plasma effects inside the gas cell and thus it is stopped before entering the gas cell whereas light beams, such as p or 3 He, can pass through the gas cell. In the light-ion ion guide, the target is inside the IGISOL gas cell, where the product recoils are stopped, and a good fraction of the ions end up with charge state 1 + . In the heavy-ion ion guide, also known as HIGISOL [31,32], the target is in front of the gas cell and the products have to recoil at small angles in order to pass through a Havar window around the beam stopper before thermalizing in the gas cell. The employed production methods are summarized in table 1.
After thermalization, the ions are extracted from the ion guide with the help of differential pumping and an electric field. The ions are accelerated to 30 keV and massseparated by a dipole magnet before entering the radiofrequency quadrupole (RFQ) [42], which is used for cooling and bunching of the ions. After the RFQ, the ions are injected into the JYFLTRAP [43] cylindrical double Penning trap situated inside a 7 T superconducting solenoid.
The first trap is called the purification trap since it is used for isobaric purification via mass-selective buffer gas cooling [44]. The precision mass measurements are carried out in the second trap, known as the precision trap, via the time-of-flight ion cyclotron resonance (TOF-ICR) method [45,46].
In the TOF-ICR method, the cyclotron frequency of the ion of interest with mass m and charge q in a magnetic field B, ν c = qB/(2πm), is compared to the cyclotron frequency of a reference ion (ν ref ) with a well-known atomic mass m ref . Since the mass-separated ions have typically the same charge state of 1 + at IGISOL, the mass of the ion of interest is obtained as: Each measurement of the ion of interest is sandwiched between two reference measurements in order to determine the value of the magnetic field B at the time of the actual measurement. Since the IGISOL method provides a large variety of possible reference ions to be measured on-line, the ion with a superior precision closest to the ion of interest is typically chosen for reference. In some cases, the production rate of oxides can be higher or comparable to the rate of the ions. For example, the masses of neutrondeficient yttrium, niobium and zirconium isotopes have been measured as oxides.
The data have been fitted and analysed mainly with the programs LAKRITSI and COMA [28]. A count-rateclass analysis [47] has been performed whenever possible. The uncertainty contribution of possible magnetic field fluctuations has been added, and mass-dependent and residual uncertainties have been included in the final atomic-mass values. A detailed description of the data analysis can be found in ref. [19]. The latest results for the mass-dependent and residual uncertainties applicable to the measurements performed after the June 2007 magnet quench are reported in the JYFLTRAP paper on carboncluster cross-reference measurements [48].

Mass measurements at A = 23 and A = 31
The mass measurements at A = 23 and A = 31 have been motivated by nova nucleosynthesis [12] and the Isobaric Multiplet Mass Equation (IMME) (see, e.g., ref. [49,50]). According to the IMME, the masses of members with an isospin projection T Z = (N −Z)/2 of an isobaric multiplet T should lie along a parabola M (T, T Z ) = a+bT Z +cT 2 Z . In general, the IMME has worked well and it has been used to predict masses of more exotic members of the multiplet. A breakdown of the IMME could be explained, for example, by higher-order perturbations or by the importance of including three-body terms. In addition, a significant component of isospin mixing could also result in deviations from the quadratic behaviour [51].
At JYFLTRAP, the masses of 23 Al and 23 Mg have been determined precisely against the reference nuclide 23 Na. The new mass value for 23 Al is 22 (19) keV lower and 55 times more precise than the AME03 [52] value.
The JYFLTRAP mass value for 23 Mg agrees with the AME03 value [52] and almost doubles the precision. The most recent ground-state masses for 23 [52], and excitation energies for the T = 3/2 isobaric analog states [53,54] were adopted and a quadratic IMME fit (χ 2 /n = 0.28) was performed for the T = 3/2 quartet at A = 23 in ref. [26]. The cubic fit yielded a cubic term d = 0.22 (42) keV consistent with zero. Thus, the IMME was found to work well in the A = 23 quartet.
Another interesting T = 3/2 quartet lies at A = 31: 31 Si, 31 P, 31 S, and 31 Cl. For this quartet, the mass of 31 S has been precisely measured at JYLFTRAP and was found to deviate from the AME03 value [52]. Unfortunately, an attempt to measure the mass of the much more uncertain 31 Cl nucleus failed due to overwhelming nitrogen oxide background at A = 31 caused by poor vacuum conditions in the IGISOL facility during that run. In the future, a mass measurement of 31 Cl would be very interesting at the new IGISOL-4 facility.
Currently, the only isobaric quintet that has been measured precisely enough to test the IMME lies at A = 32. Although there have been no mass measurements at A = 32 at JYFLTRAP, the IMME at A = 32 has been studied in one of our publications [27]. A recent 32 S( 3 He, t) 32 Cl measurement [55] showed a discrepancy to the 32 Cl mass obtained from the proton separation energy [56] and the 31 S mass from AME03. The mass of 31 S measured at JYFLTRAP was found to deviate from AME03 [52] by 2.1(15) keV. When our new mass value is combined with the proton separation energy of ref. [56], a mass excess value, which is more precise than the previous measurements and agrees with the adopted AME03 value, is obtained for 32 Cl. In ref. [27], the quadratic IMME fit was performed with six different data sets corresponding to two different values of 32 P [52,57] and three different values of 32 Si [52,[57][58][59]. The overall result of the quadratic fits is that the IMME fails significantly (χ 2 /n > 6.5) in all data sets. The cubic term d was found to depend strongly on the data set: the values varied from d = 0.51 (15) keV to d = 1.00 (13) keV. In the future, further mass measurements of 32 Ar, 32 Cl, 32 P, and 32 Si, should solve these discrepancies and really validate the breakdown of the IMME.

Mass measurements around 56 Ni
Mass measurements around the doubly magic N = Z nucleus 56 Ni provide essential data for the studies of, e.g., isospin symmetry, mirror nuclei, Coulomb displacement energies, neutron-proton pairing, and shell-gap energies. At JYFLTRAP, Q EC -values of the mirror nuclei 53 Co, 55 Ni, 57 Cu, and 59 Zn, as well as of the N = Z nuclei 54 Co, 56 Ni, 58 Cu, 60 Zn, and 62 Ga have been precisely measured (see refs. [37][38][39]). In addition to Q EC -values, a few proton separation energies (S p ) have been directly measured by using the (A − 1, Z − 1) nuclide as a reference for the (A, Z) nuclide [38]. In order to obtain more accurate mass measurements, a network calculation of 17 frequency ratio measurements between 13 nuclides has been performed around 56 Ni [38]. In this way, also the masses of reference nuclides, such as 55 Co and 58 Ni, and 59 Cu, could be evaluated. The obtained masses for 55 Ni, 56 Ni, and 57 Cu agree well with the AME03 values [52], but are 15, 26, and 31 times more precise, respectively.
The most significant deviations (around 2σ) to the AME03 values in this mass region have been found for copper isotopes 58 Cu (−3.6(17) keV) and 62 Cu (10.6(42) keV). The measured JYFLTRAP mass of 62 Cu is higher than the adopted AME03 value, which was based on measurements using the 62 Ni(p, n) 62 Cu reaction [60,61] and the β-decay energies of 62 Cu [62][63][64]. The first two of the three β-decay experiments [62,63] have underestimated the β-decay energy, which results in a too low adopted AME03 value.
The mass of 58 Cu has already been measured with the JYFLTRAP purification trap in 2004 [43]. The new JYFLTRAP mass value for 58 Cu agrees with the old purification trap measurement [43] but differs from the precise (p, n) threshold energy measurements [65][66][67]. However, when the (p, n) measurements are revised with the updated mass values [68] an agreement with JYFLTRAP is obtained.
Absolute deviations to AME03 are rather small in this mass region. The biggest deviations (in keV) belong to 59 Zn (47(40) keV) and 60 Zn (15(11) keV). For those cases the Q values derived from 58 Ni(p, π) 59 Zn [69] and 58 Ni( 3 He, n) 60 Zn [70] lead to slightly underestimated masses for 59 Zn and 60 Zn. In addition to these nuclides, a difference was found for the proton-decaying high-spin isomer in 53 Co: the new JYFLTRAP value is 36 (22) keV lower than in AME03 [52].
Q EC values of several T = 1/2 mirror nuclei have been measured at JYFLTRAP. These experiments have been motivated by recent studies [71,72] where corrected ft values have been calculated for T = 1/2 mirror transitions and the Conserved Vector Current Hypothesis has been tested. The Q EC values of the T = 1/2 nuclei 31 S, 53 Co, 55 Ni, 57 Cu, and 59 Zn have been measured with a precision of better than 0.7 keV at JYFLTRAP [27,38]. In addition, the Q EC value of 53 Co m [38] has been measured with a precision of 1.2 keV. The largest differences to the AME03 values have been found at 53 Co m and 59 Zn. The Q EC values of 45 V and 49 Mn have been measured in 2010 but the results have not yet been published. In the future, these measurements will be continued with 47 Cr and 51 Fe.
In addition to the T = 1/2 mirror nuclei, the Q EC values of the T = 1 nuclei 56 Ni, 58 Cu, and 60 Zn have been measured at JYFLTRAP. Interestingly, the JYFLTRAP Q EC value of 58 Cu was found to be 4.6(15) keV lower than in AME03. This Q EC value has to be taken into account in studies of isospin symmetry among A = 58 nuclei [73].
There have been no mass measurements for the rpprocess between 62 Ga and 80 Y at JYFLTRAP. This region has been quite well covered by other Penning traps. At ISOLTRAP, Ga, Se, Br, Kr, Rb, and Sr isotopes have been extensively studied [74][75][76][77][78][79]. Ga, Ge, As, Se, and Br isotopes relevant for the rp-process have been determined with LEBIT [18,80], and Se, As, and Ge isotopes at A = 68 with CPT [81].
The mass measurements conducted at JYFLTRAP in this mass region have revealed large deviations to the AME03 values. Many of the measured mass excess values, for example, 83,85 Zr and 85−88 Nb, have earlier been based on β-decay endpoint energies, which have a tendency to underestimate the masses due to unobserved feeding to higher-lying states in the daughter nuclides (pandemonium effect [87]). This problem is likely to play a stronger role in nuclides further from stability. Thus, the more exotic the nuclide, the more it typically deviates from the JYFLTRAP value (see fig. 2). The yttrium isotopes do not follow this trend since the AME03 value for 80 Y is based on a direct time-of-flight mass measurement at the ISN SARA cyclotron [88]. The mass of 86 Zr in AME03 is based on 90 Zr(α, 8 He) 86 Zr reactions [89] and not on βdecay energies. Many nuclides -84 Zr, 88,89 Tc, [90][91][92] Ru, [92][93][94] Rh, and 94−95 Pd-have been measured for the first time at JYFLTRAP. As can be seen from fig. 2, the extrapolated mass excess values of AME03 are typically too small. In other words, JYFLTRAP has found these nuclei to be less bound.
In the mass region below Z = 50, the mass excesses of [89][90][91][92] Tc, [90][91][92]94 Ru, [92][93] Rh as well as 99,101 Ag, [101][102][103][104] Cd, [102][103][104][105] In have been measured with the SHIP-TRAP Penning trap at GSI [19,90]. In general, SHIP-TRAP and JYFLTRAP results agree well with each other (see fig. 3). Small differences are found for 92 Tc (Δ S−J = 15(12) keV) and 90 Ru (Δ S−J = 17(11) keV). Differences are also found for 101,102,104 Cd, where ISOLTRAP data [17] are in agreement with JYFLTRAP, not with SHIPTRAP. Many of these masses have also been measured with CPT but the preliminary graphical data [91] for 90 Many open questions concerning the neutron-deficient nuclides around A = 80-100 remain. For example, whether an observed state is a pure ground state, an isomeric state, or a mixture of these should be investigated and verified for some of the measured nuclides. Corrections due to a possible mixture of ground and isomeric states or due to unknown level scheme have been applied according to eq. (14) of ref. [93] and have been added quadratically to the experimental uncertainties for the nuclei listed in table 2. However, in some cases isomers might not be known, or information is uncertain. For example, no correction has been applied to 86 Nb (E x = 250(160)# keV [94]) since this isomer is considered as uncertain. Clearly more experiments are needed to clarify the low-lying level structure of nuclides in this mass region, and revisions of some mass values might become necessary as a consequence.

Mass measurements above 100 Sn
Masses of 104-108 Sn, [106][107][108][109][110]  104 Sn: The mass of 104 Sn has been previously measured via β-decay endpoint energies [99,100]. It can also be determined from the α-decay energy of 108 Te [103][104][105][106]. The β-decay results and the Q α -values from refs. [104,105] agree with the JYFLTRAP result but the α-decay energies from refs. [103,106] differ from it. The AME03 value, which is mainly based on the α-decay energies, is significantly lower than the JYFLTRAP value. 105 Sn: The mass of 105 Sn can be determined from the Q α -values of 109 Te [103][104][105][106]. The Q α -values from refs. [104,105] agree with the JYFLTRAP result but as in the case of 104 Sn the values from refs. [103,106] differ: Q α from ref. [103] is around 40 keV smaller and the value from ref. [106] is around 30 keV higher than the Q α -value obtained with JYFLTRAP. The JYFLTRAP result agrees with the β-endpoint measurement of 105 Sn [101] and the SHIPTRAP value [90]. 106 Sn: The Q EC value of 106 Sn from ref. [99], the Q α -value of 110 Te from ref. [105] and the SHIPTRAP value [90] agree well with the result obtained at JYFL-TRAP. However, the values based on the Q EC -value from ref. [102] and the Q α -value of 110 Te from ref. [107] differ slightly from the JYFLTRAP mass excess value for 106 Sn. As a result, the AME03 value differs from the JYFLTRAP value.
107 Sn: The mass of 107 Sn has earlier been based on the mass ratio measurement of 107 Sn to 106 Sn [111]. The mass value determined at JYFLTRAP agrees well with it.
108 Sn: The β-delayed proton decay of 109 Te [109], the mass ratio of 108 Sn to 107 Sn [111], and the AME03 value [52] disagree slightly from the JYFLTRAP value. The result from the β decay of 108 Sn [102] and the direct mass measurement performed at ESR [110] agree very well with JYFLTRAP. The differences between the JYFLTRAP and the AME03 mass excess values for 109 Te and 107 Sn explain why the mass excess values for 108 Sn derived from refs. [109,111] differ from the AME03 value (see fig. 4). 106 Sb: The mass of 106 Sb has been measured for the first time with JYFLTRAP and the result agrees with the extrapolation based on systematic trends in AME03 [52]. 107 Sb: The mass of 107 Sb has been directly measured at SHIPTRAP [90]. The value differs from the JYFLTRAP value by 17 (12) [52] based mainly on ref. [109] is significantly higher than the JYFLTRAP mass excess value. 111 I: The mass of 111 I has also been measured at SHIP-TRAP [90] and it agrees with JYFLTRAP. It can also be determined from the Q α -values of 111 I [ [103][104][105]113] with the mass of 107 Sb. The measurements agree with the present data except for the result from ref. [113].

Energy systematics: S p -, Q α -, and S 2p -values
Proton separation energies (S p ) are important for the calculations of proton capture rates and for the modeling of the astrophysical rp-or νp-processes, since the proton capture rates and obtained abundances depend exponentially on the S p -values. At JYFLTRAP, the mass excesses for both the (A, Z) and (A − 1, Z − 1) nuclides, and thus the S p -values, have been determined for 41 nuclides. The measured masses have an impact on altogether 138 S p -values. For 56 Ni, 57 Cu, 59 Zn, and 60 Zn, a sub-keV precision in the proton separation energy has been achieved by using the (A − 1, Z − 1) nuclide as a reference in the mass measurement. Figure 7 shows a comparison of the S p -values calculated entirely from JYFLTRAP masses with the values of AME03.
The biggest deviations in the proton separation energies compared to the AME03 values are found for Nb, Tc, Zr and Mo isotopes (see table 3). In addition, the S p -values of 58 Cu, 59 Zn, 60 Zn, 88 Nb, 104 In, and 109 Sb differ slightly from AME03 (see fig. 7). The deviations to the AME03 values are new experimental data may change those values dramatically. In addition, the S p -values for 62 Cu, 63 Zn, 82-83 Y, 86 Zr, and 106,108 Sn disagree with the AME03 values. In the lighter mass region, the S p -values for 23,26 Al, [26][27] Si, 31 S, 34 Cl, 42 Ti, and 46 V differ from the AME03 values.
In the SnSbTe region, α separation energies become sufficiently small for α decay to become energetically possible, and for (p, α) and (γ, α) reactions to play an important role in astrophysical environments. Q α -values are therefore needed. The Q α -values of 108,109 Te and 111 I have been precisely determined at JYFLTRAP by measuring the masses of the corresponding mother and daughter nuclides (see table 4). The JYFLTRAP Q α -value for 108 Te is significantly lower than in AME03. By combining the results of JYFLTRAP [3,41] with SHIPTRAP [90], also the Q α -values for 105-108 Sn and 106-109 Sb, [110][111][112] Te, 112-113 I, and 113 Xe have been obtained. For these Q α -values, deviations to AME03 are found for 108 Sn, 109 Sb, and [110][111][112] Te.
Two-proton separation energies S 2p plotted against the proton number Z often show continuous and smooth Table 3. The largest observed differences (in keV) to the AME03 proton separation energies at JYFLTRAP. For the nuclides marked with a , the Z − 1 nuclide has not been measured at JYFLTRAP and AME03 has been adopted. The mass excesses for the nuclides marked with b have been adopted from AME03 but the corresponding Z − 1 nuclides have been measured with JYFLTRAP. "#"; denotes that the used AME03 value is based on extrapolations. The big deviations for 86 Table 4. Qα-values from JYFLTRAP mass measurements [3,41] combined with the SHIPTRAP results [90], and comparison to the literature values [52]. Only alpha decays for which both the mother and daughter have been measured at JYFLTRAP and/or SHIPTRAP and at least either of them has been measured at JYFLTRAP have been taken into account.
(keV) (keV) (keV) 105 Sn 74 (5) (50) respective isotonic chains (blue line for N = 43 and red line for N = 44). The masses of 85 Mo and 87 Tc have then been measured at SHIPTRAP and big deviations of 1590(280) keV and 1430(300) keV from AME03 have been found [116]. When the SHIPTRAP values are adopted, the S 2p values follow largely the systematic trend (see fig. 8).
The strong deviations between AME03 and new mass measurements in this region, and in particular the observed dramatic change in systematic trends and the disappearance of irregularities when using new Penning-trap masses casts doubt on the remaining AME03 masses and the resulting AME03 S 2p trends in this region. More mass measurements towards more exotic isotones are urgently needed to verify or correct the AME03 data. Such measurements would also be important to show whether the linear trend in S 2p -values continues or whether there are indications of deformation. For example, in-beam gamma spectroscopy experiments have shown that almost all nuclei from krypton (Z = 36) to niobium (Z = 41) have permanent deformation when N < 44 [117].
Mass measurements around 100 Sn offer a possibility to determine the Z = 50 proton shell-gap energy E gap,Z=50 from two-proton binding energies: E gap,Z=50 = S 2p (Z = 50)−S 2p (Z = 52) (see fig. 9). Penning-trap mass measurements performed at JYFLTRAP [3,41], SHIPTRAP [90], and ISOLTRAP [17] improve the precisions of the shellgap energies a lot and reveal deviations from the AME03  [52]. The data from SHIPTRAP [90,116] and ISOLTRAP [17] have been taken into account in the Penning-trap data whenever possible. The "TRAP" data cover the S 2p-values where at least one data set comes from a Penning-trap measurement and the missing data have been adopted from AME03. The "AME03" values are based only on AME03. "#" marks that the used values at N = 56-60. With the new trap data a minimum in the shell-gap energies is achieved at N = 59, and it is broader than with the AME03 data where a deeper minimum at N = 58 is observed. Both data show an increasing shell-gap energy when proceeding towards the magic neutron number N = 50.

Nucleosynthesis in novae
Novae occur in binary systems consisting of a white dwarf accreting hydrogen-rich matter from a main-sequence companion. Thermonuclear explosions of the accreted envelope drive the nova phenomenon. Novae on particularly massive oxygen-neon white dwarfs (ONe novae) are thought to reach peak temperatures of up to 4 × 10 8 K. Under these conditions the explosive hydrogen burning occurs as a sequence of proton captures and β + decays (and sometimes (p, α) reactions) proceeding up to A = 40 due to the presence of NeNa-MgAl seed nuclei (see refs. [10][11][12][13]118]). Of special interest in ONe novae is the production of 22 Na and 26 Al, which are sufficiently long-lived radioactive isotopes for their decay γ-radiation to be potentially observable. 22 Na (T 1/2 = 2.6019(4) y [119]) de-cays into a short-lived excited state of 22 Ne which deexcites to its ground state by emitting a 1.275 MeV γ-ray. Although several attempts to observe these γ-rays from nearby novae have been made, only an upper limit of the ejected 22 Na has been obtained [118]. The 26 Al ground state (T 1/2 = 7.17(24) × 10 5 y [119]) decays to an excited state of 26 Mg at 1.809 MeV. The γ-rays following the deexcitation of this state have been observed with γ-ray telescopes but the half-life is too long to associate them with a particular astrophysical event. The general distribution of Galactic 1.809 MeV activity indicates an origin mainly associated with massive stars, but it is important to determine a possible nova contribution. 22 Na is produced in a so-called NeNa cycle where 20 Ne(p, γ) 21 Na is followed either by proton capture 21 Na (p, γ) 22 Mg(β + ) 22 Na or β decay 21 Na(β + ) 21 Ne(p, γ) 22 Na(β + ) 22 Ne(p, γ) 23 Na(p, α) 20 Ne. In order to model the production of 22 Na, the destruction channels, such as 22 Mg(p, γ) 23 Al and 22 Na(p, γ) 23 Mg have to be known precisely. At JYFLTRAP, 23 Al was found to be 22 (19) keV more proton-bound [26] than in AME03 [52]. Thus, the resonant contribution for the rate of 22 Mg(p, γ) 23 Al is little higher, and 23 Al is more resilient to destruction through photodissociation. Also the mass of 23 Mg has been measured at JYFLTRAP [26] but its impact on the Fig. 9. Proton shell-gap energies at Z = 50 determined from two-proton separation energies. Recent Penning-trap data from JYFLTRAP [3,41], SHIPTRAP [90], and ISOLTRAP [17] have been adopted whenever possible. The "TRAP" data cover the values where at least one data set comes from a Penning-trap measurement and the missing data have been adopted from AME03. The "AME03" data points are based only on AME03. "#" marks that the used AME03 value is based on extrapolations. calculated resonant rate for the 22 Na(p, γ) 23 Mg reaction has not been investigated. 26 Al is produced in a so-called MgAl cycle: 24 Mg(p, γ) 25 Al(β + ) 25 Mg(p, γ) 26 Al g.s. (β + ) 26 Mg(p, γ) 27 Al(p, α) 24 Mg. The production of 26 Al g.s. can be bypassed via 25 Al(p, γ) 26 Si(β + ) 26 Al m (β + ) 26 Mg. Therefore, the rate for the proton capture reaction 25 Al(p, γ) 26 Si is extremely important to constrain the model [118]. The JYFLTRAP mass value of 26 Si results in a 3.7(31) keV lower proton separation energy for 26 Si than in AME03 [52]. This changes the calculated stellar reaction rates of 25 Al(p, γ) 26 Si by about 10% [33] compared to the rates calculated with the values from ref. [120].
The reaction 30 P(p, γ) 31 S plays a crucial role governing the flow towards 32 S and heavier species in novae [11,118]. At 30 P, the reaction flow has to proceed either via 30 P(p, γ) 31 S(p, γ) 32 Cl(β + ) 32 S or via 30 P(p, γ) 31 S(β + ) 31 P(p, γ) 32 S. The 30 P(p, γ) 31 S rate also has an effect on the 30 Si abundance [11]. The lower the proton capture rate, the more favorable is the β + decay of 30 P and more 30 Si is produced. A more accurate reaction rate and 30 Si abundance (or 30 Si/ 28 Si abundance ratio) helps in the identification of presolar grains with a possible nova origin [121]. The proton separation energy obtained at JYFLTRAP [27] is 2.1(16) keV lower than the adopted value [52]. Although the difference is quite small, it has an effect on the calculated reaction rate of 30 P(p, γ) 31 S which has been studied, for example, in refs. [122][123][124][125].
Although in both cases the impact on the reaction rates is small, and there are much larger uncertainties from poorly known excited states, the measurements are a step towards more reliable rates that will be of particular importance once resonance parameters have been measured in future experiments. More importantly however, precise masses are essential for carrying out planned direct reaction rate measurements at radioactive beam facilities. Such experiments inherently suffer from limited beam intensities and resonance energies must be known precisely to make experiments feasible.

νp-process
The astrophysical νp-process has been suggested to occur in supernovae and possibly in gamma-ray bursts where proton-rich ejecta are created by strong neutrino fluxes [6,7]. In principle, it proceeds similarly to the rp-process as a sequence of proton captures and β + decays but the flow towards heavier elements is accelerated via fast (n, p) reactions bridging the slow β + decays along the path of the rp-process. The neutrons needed for the (n, p) reactions are created by antineutrino absorptions on protons. Nuclei with mass numbers A > 64 are produced in the νp-process, which has been proposed to be a candidate for the origin of solar abundances of light p nuclei 92,94 Mo and 96,98 Ru [6].
The νp-process has been modeled with the JYFLTRAP mass values [19,40] in ref. [19]. The JYFLTRAP mass excess value for 88 Tc was found to be 1031(218) keV higher than in AME03 [52]. The heavier 88 Tc means a lower proton separation energy for 88 Tc, which increases the reaction rate of 88 Tc(γ, p) 87 Mo and suppresses the flow through 87 Mo(p, γ) 88 Tc. The main reaction flow to nuclei with A > 88 proceeds then through 87 Mo(n, p) 87 Nb (p, γ) 88 Mo(p, γ) 89 Tc. The stronger reaction flow through 87 Mo(n, p) 87 Nb and a higher abundance of 87 Nb enables also a flow through 87 Nb(n, p) 87 Zr which is seen in the abundance pattern as an increased abundance of 87 Sr [19].
A recent mass measurement of 87 Mo [116] revealed a deviation of 810(220) keV to the AME03 value. With the new mass values for 87 Mo [116] and 88 Tc [19], the proton separation energy of 88 Tc is in agreement with the AME03 value: the difference is 220(320) keV. This obviously changes the modeling results and further demonstrates the importance of accurate mass measurements.
Another example for the impact of the new mass values is 90 Tc. The average mass measured at JYFLTRAP and SHIPTRAP [19] is 486(240) keV higher than the AME03 value based on the β-decay energies. A lower proton separation energy increases the reaction rate of 90 Tc(γ, p) 89 Mo slightly. This, in turn, shifts some abundance from the A = 90 chain into the A = 89 chain and shows up in the abundance pattern as a decrease for 90 Zr [19].
The νp-process has been proposed to be a candidate for the origin of the solar abundances of the light p nuclei 92,94 Mo and 96,98 Ru [6]. Of special interest is the relative production of 92 Mo and 94 Mo governed by the proton separation energy of 93 Rh. The more proton-bound 93 Rh, the more 94 Pd, and in the end, more 94 Mo will be produced. In order to obtain the observed solar abundance ratio of 92 Mo and 94 Mo in current νp-process models it has been suggested that the proton separation energy of 93 Rh should be very close to 1.65 MeV [126]. The JYFLTRAP and SHIP-TRAP mass measurements [19] yield a proton separation energy S p = 2001(5) keV in agreement with the result from the Canadian Penning Trap S p = 2007(9) keV [21]. However, the experimental results disagree with the value needed for solar 92 Mo/ 94 Mo ratio in supernova outflows. This suggests that supernova outflows do not exclusively produce both molybdenum isotopes or that the winds are qualitatively different from the current supernova models [126].
The impact of mass variations on the abundances and production path of the νp-process has been investigated in ref. [20]. There, 93 Pd, 100 Cd, and 101 In were found to have highest influence on the final abundances and path. In addition, varying the mass excess of 80 Zr by 2σ has a huge impact on the νp-process modeling due to large experimental mass uncertainty of 80 Zr (1490 keV) [20]. These nuclides will be searched for at IGISOL-4.

rp-process
Explosive hydrogen burning at temperatures in excess of 10 8 K via the rp-process was first introduced in ref. [1]. Astrophysical sites where such burning occurs are X-ray bursts and, to a limited extent, novae. In this rp-process [1,2], the rapid proton captures on seed nuclei or on the products of helium burning lead to a production of heavier elements. Proton captures will proceed until they are inhibited by a low or negative Q-value, which leads to substantial (γ, p) photodisintegration. At those points, the rpprocess has to wait for a much slower β + decay to happen. If the half-life of the β-decaying nucleus is particularly long the nucleus is called a waiting point.
Nuclear masses are relevant for the modeling of the rp-process due to the exponential dependence of effective waiting-point lifetimes on binding energy differences. The isotonic abundance ratios are exponentially dependent on proton separation energies as shown by the Saha equation (see, e.g., ref. [16]). The impact of mass uncertainties on the rp-process has been studied, for example, in refs. [15,20]. In ref. [15], a list of nuclides whose masses should be measured in order to more reliably model the rp-process in X-ray bursts is given. From that list, the masses of 106 Sb and 107 Sb have already been determined at JYFLTRAP [3], and interesting (but also experimentally challenging) candidates for future mass measurements at JYFLTRAP are 31 Cl, 56 Cu, 61 Ga, 83,84 Nb, 86 Tc, 89 Ru, 90 Rh, 99 In, 96 Ag, 97 Cd, and 103 Sn.
The impact of mass variations on the light curve, the final abundances (ashes) and path of the rp-process in Xray burst was modeled in ref. [20]. 94 Ag, 93 Pd, and 91 Rh were found to have highest influence on the nucleosynthesis modeling. In particular, the reaction 93 Pd(p, γ) 94 Ag has the strongest effect on the simulation of X-ray burst lightcurve. The sensitivity of the flow ratio between 93 Pd and 94 Ag is an indication of forward and backward flows of similar order of magnitude, and thus, suggests that 93 Pd is a waiting point [20]. JYFLTRAP aims to measure the masses of 93 Pd and 94 Ag in future.

Doubly magic waiting point 56 Ni
A typical duration of an X-ray burst is 10-100 s. 56 Ni decays under terrestrial conditions mainly by electron capture. Electron densities during the rp-process are much smaller than in atoms, leading to a very long half-life of the order of at least 10 h making 56 Ni essentially stable for typical rp-process timescales. Because of its doubly magic character the proton capture Q-value of 56 Ni is relatively low, making it a potentially unique rp-process waiting point that cannot be overcome by β + decay. Indeed, historically 56 Ni was considered as an endpoint of the rpprocess [1]. However, with modern nuclear masses the proton capture Q-value is sufficienly high that 56 Ni only becomes a waiting point for temperatures in excess of around 2 GK [2,127]. Nevertheless, such temperatures are reached in some X-ray burst models, leading to a temporary stalling of the rp-process. The onset of processing beyond 56 Ni during the cooling of the burst depends sensitively on the exact Q-value for the 56 Ni proton capture. This Qvalue has been directly measured at JYFLTRAP by using 56 Ni as a reference for 57 Cu in the mass measurement. In this way, the accuracy of the proton-capture Q-value was improved from 695 (19) keV [52] to 689.69(51) keV [38].
Since the calculated resonant reaction rate to a state at an energy E x is exponentially dependent on the resonance energies E r = E x −Q p,γ , the uncertainty of the proton capture Q value has a large effect on the uncertainty of the 56 Ni(p, γ) reaction rate. With the new Q-value, a factor of four in the uncertainty of the reaction rate at temperatures around 1 GK shown in ref. [127] is removed and the new rate is a little higher than the one calculated with the old Q value. The new Q-value supports the conclusions of ref. [127] that the lifetime of 56 Ni against proton capture is much shorter than in the previous works. This reduces the minimum temperature required for the rpprocess to proceed beyond 56 Ni. This temperature threshold coincides with the temperature for the break out of the hot CNO cycles with the rates of ref. [127]. Therefore, the rp-process can always proceed beyond 56 Ni provided a sufficient amount of hydrogen is present.

Quenching of the SnSbTe cycle
The JYFLTRAP value for the proton separation energy of 106 Sb, S p = 424(8) keV, disagrees considerably with the value S p = 930(210) keV [128] based on the alphadecay energies and the mass of 114 Cs determined from its β-delayed proton decay. The value of ref. [128] has been considered erroneous already in AME03 [52], where an extrapolated value of S p = 360(320)# keV agreeing with JYFLTRAP is given for 106 Sb. The consequences of the new proton separation energies of 106 Sb and other nuclides in the SnSbTe region at JYFLTRAP, have been investigated in ref. [3] with the same one-zone model as in ref. [129]. In ref. [129], 105 Sb was found proton unbound with S p ( 105 Sb) = −356 (22) keV based on α-decay energies and the dependence of the branching into the SnSbTe cycle was plotted against the proton decay Q-value. Due to proton-unbound 104,105 Sb the rp-process has to proceed along the tin isotopes to 105 Sn. There, the proton capture probability depends on its Q (p,γ) -value, in other words, on the proton separation energy of 106 Sb. With the new JYFLTRAP value for S p ( 106 Sb), only 3% of the reaction flow branches into the SnSbTe cycle at 105 Sn, thus considerably attenuating the cycling via the chain 105 Sn-106 Sb-107 Te-103 Sn-103 In-104 Sn- 104 In-105 Sn.
The proton-separation energy of 107 Sb is also quite low, 588(7) keV, and only 13% branching to the SnSbTe cycle is found at 106 Sn. Since the β-decay half-life of 106 Sn is long (2.1 min), it inhibits further processing towards 107 Sn and 108 Sb, although the proton separation energy of 108 Sb (1222(8) keV) would be high enough for branching into the SnSbTe cycle.
Previous rp-process calculations had assumed there is a strong SnSbTe cycle where proton captures on 105 Sn and 106 Sb lead to 107 Te, which then α decays back to 103 Sn creating helium and cycling the matter between Sn, Sb and Te isotopes. This cycle resulted in a large accumulation of the longest-lived isotope in the SnSbTe cycle, 104 Sn. This was also seen in the final composition of the burst ashes where 104 Pd was the most abundant element.
With the new JYFLTRAP mass values the SnSbTe cycle develops closer to stability and requires therefore longer processing to be reached. Model calculations indicate that even under the most favorable conditions it is unlikely that a substantial SnSbTe cycle can develop in an X-ray burst. As a result, the final composition of the ashes is characterized by a much broader distribution of 68 Zn, 72 Ge, 104 Pd, 105 Pd, and residual helium with comparable abundances. The absence of a strong SnSbTe cycle also reduces late-time 4 He production, which reduces the latetime boost of hydrogen consumption and the associated rise in energy production. This leads to a slightly longer, less luminous tail. However, the effect is small since the Sn isotopes are reached at a very late stage in the burst. The quenching of the SnSbTe cycle leads also to a reduction of residual 4 He and 12 C.
Although the masses needed to constrain the reaction flow in the SnSbTe cycle are now mostly well known, uncertainties remain in the proton capture rates on the antimony isotopes, in particular 105 Sb and 106 Sb. It has been estimated that the proton-capture rate uncertainties vary up to a factor of 3 close to stability and the uncertainties far from stability might be larger [130]. For example, the 106 Sb(p, γ) rate calculated with the code from ref. [131] is about a factor of 4 larger than the NON-SMOKER [132] rate used in ref. [3].

rp-process modeling with updated masses
To explore the impact of recent Penning-trap mass measurements, including the JYFLTRAP measurements, on the rp-process in X-ray bursts, and to explore the impact of remaining uncertainties, we carried out model calculations with the one-zone X-ray burst model from [20,133]. Models employing the one-zone approximation reproduce the composition of the burst ashes and some general features of the burst light curve quite well, and at the same time allow to explore the impact of variations in the nuclear physics input in a computationally efficient way. The impact of mass uncertainties on X-ray burst models has been studied before using the post-processing approximation [15], which neglects the impact of modified nuclear physics on energy generation. Other work has been based on the same model employed here, but masses were varied within quoted 1σ errors in a random way [20].
Here we choose a different approach with the goal to illustrate the maximum possible impact that mass uncertainties can have on burst model predictions. To that end, we carry out two calculations for each set of masses, one where all proton capture Q-values are simultaneously increased by 3σ, and one where they are all simultaneously decreased by 3σ. 3σ might seem like a large variation. However, for the Penning-trap mass measurements, error bars are so small that even a 3σ variation has no significant effect on the model. On the other hand, for theoretically predicted masses, for example from Coulomb shifts, or for masses determined with other experimental methods, such as β-endpoint measurements, systematic errors make such large deviations more likely than they might appear based on a Gaussian probability distribution. In addition, the effects of masses on the rp-process can be highly non-linear. Changes in the observables for 1σ mass variations can therefore not simply be scaled to estimate the impact of large variations due to systematic errors. Previous sensitivity studies therefore likely underestimated the impact of mass uncertainties and have probably not identified all critical masses. Our study is therefore complementary to previous approaches -while it is not intended to provide statistically correct error bars for observables, it will identify all possible mass uncertainties and provide an envelope for observables that takes into account non-linearities and the possibility of systematic, non-Gaussian errors.
We ran calculations with three sets of masses: AME03, AME10, and NOJYFL. AME03 includes experimental and extrapolated masses from AME03, and uses Coulomb Shifts [134] to calculate the masses of more exotic nuclei with Z > N. AME10 uses in addition all Penning-trap mass measurements in the rp-process region that have been published through 2010 (see fig. 1). Recently published results [79,116,135] were not included in the calculations. NOJYFL is similar to AME10 but we removed all masses that have been measured by JYFLTRAP to illustrate the impact of the JYFLTRAP program.
The rp-process reaction paths for the AME10 upper and lower proton capture Q values are shown in fig. 10. Clearly, current mass uncertainties still allow for very large changes in the reaction paths. For the low Q-values the path below ruthenium is shifted by one mass unit, above ruthenium by 2 mass units closer to stability. With the low Q-values the 80 Zr waiting point is completely bypassed as the reaction flow proceeds towards stability in  the yttrium isotopic chain. While JYFLTRAP mass measurements have made the formation of a SnSbTe cycle much more unlikely, the high Q-value calculation does develop such a cycle at 103 Sn because of the large uncertainties (300# keV and 360# keV) that still exist for the 103 Sn and 104 Sb masses. While a significantly proton bound 104 Sb, which would be required to form a SnSbTe cycle, seems unlikely given the trend of the measured proton separation energies of less neutron-deficient Sb isotopes, tentative experimental results indeed hint at 104 Sb not being a fast proton emitter [129]. Figure 11 demonstrates that the burst light curve can be influenced dramatically by nuclear masses. At the extreme of very high Q-values, the major waiting points can be bypassed efficiently and processing towards heavy nuclei during the burst cooling phase when the luminosity is decreasing is greatly accelerated leading to a significant increase in energy generation, and fast exhaustion of fuel. The result is the development of a shoulder in the light curve during the early cooling phase, and a second peak in the burst profile after about 70 s. On the other hand, very low Q-values increase photodisintegration, which hampers proton capture and results in a slower rp-process closer to stability. As a consequence, energy is generated at a reduced rate, but for a longer time leading to a very long burst tail lasting about 5 minutes past the initial burst peak. Clearly Penning-trap mass measurements since 2003 have not yet reached the majority of rp-process masses and do reduce the uncertainty only somewhat. It should be noted that the systematic AME03 mass extrapolations play an important role in the model calculations. These extrapolations were based on the AME03 experimental data sets. Mass measurements since 2003 would likely lead to improved extrapolations and more reliable burst calculations. This effect is not included here, and its exploration   fig. 12 but for X-ray burst calculations with AME10 and NOJYFL. The left part of the data pairs belongs to NOJYFL (black) and the right part to AME10 (red).
needs to wait for the publication of the next Atomic Mass Evaluation. Figures 12 and 13 illustrate corresponding variations in the final composition of the ashes. The composition is given as a function of mass number, as the ashes decay along a mass chain until the first stable isotope is reached. Clearly significant variations up to an order of magnitude are possible, but not more. For many mass numbers, the maximum variations are much smaller. Among the important most abundant isotopes in the ashes, Penning-trap mass measurements since 2003 had the largest impact on the A = 68, 91, 92, 105, 106 isobars where uncertainties in the final abundance were drastically reduced (see fig. 12). The JYFLTRAP mass measurements had a major impact on all of these, with the exception of A = 68 (see fig. 13).
The reduction of the A = 92 abundance uncertainty is particularly important in light of the interest in a possible production of 92 Mo in the rp-process.

Outlook
Mass measurements on neutron-deficient nuclides of astrophysical interest will continue with JYFLTRAP at the new IGISOL-4 facility. There will be more beam time available since the two cyclotrons, MCC-30 and K-130, can work in parallel. The new facility should also offer better and cleaner conditions for mass measurements. A permanent yield station and a post-trap spectroscopy setup will help in monitoring the experiments. Besides IGISOL-4 there have been major developments in the JYFLTRAP mass measurements since the first measurements of rp-process nuclei [40]. A new fast cleaning procedure to produce isomerically pure ion samples has been developed [37]. The Ramsey method of time-separated oscillatory fields [136,137] has been successfully applied to short-lived ions of astrophysical interest. Precise data on mass-dependent and residual uncertainties of JYFLTRAP have been obtained via carbon cluster measurements [48]. Interleavedly performed measurements [34] reduce the uncertainty due to temporal B-field fluctuations, which will result in a promising improvement on future mass measurements for neutron-deficient nuclei.
With the light-ion guide at IGISOL-4, nuclides important for modeling the explosive hydrogen burning in ONe novae as well as for testing the IMME, such as 27 P, 31 Cl, and 32 Cl, will be produced. Also the Q EC -value measurements of mirror nuclei will be continued. In the heavier mass region, proton or 3 He beams on a 92 Mo target could help in populating the low-spin isomers in 91 Tc and 93 Ru. More exotic species, such as the N = 50 isotones 93 Tc, 97 Ag, 98 Cd, 99 In, and 100 Sn could be searched for with the heavy-ion ion guide. In addition, a mass measurement of the waiting-point nucleus 80 Zr would be very interesting. The masses of 94 Ag and 93 Pd have been shown to have a high impact on rp-process models, and thus should be measured. 93 Pd could be produced at HIGISOL whereas for 94 Ag, a special hot cavity laser ion source has been developed [138]. Since the half-life of the 94 Ag ground state is only around 30 ms, it is too short-lived for measurements at JYFLTRAP. However, the much longer-lived isomeric states (7 + , 0.55(6) s [139]) and (21 + , 0.40(4) s [139]) could be measured. Of these, the 21 + spin-gap isomer has gained much interest recently due to its claimed two-proton decay [140].
Taking into account all the developments carried out at JYFLTRAP and IGISOL, new mass measurements of Y, Nb, Mo, and Tc isotopes at the heavy-ion ion guide at IGISOL-4 would be relevant. These measurements would confirm the nature of the measured state (ground state or isomer) in previous experiments [19,40,116]. In addition, the few nuclides ( 92 Tc, 90 Ru, 107 Sb, and 109 Sb) for which deviations to the SHIPTRAP values have been found, could be reinvestigated.
More accurate mass values would be obtained via networks of mass measurements, where a single reference atom would not play such a big role. This would also give better information on the mass surface and be useful for mass predictions. In addition, direct frequency ratio measurements between proton capture mother and daughter would result in more precise proton capture Q-values. Identification of the ground and isomeric states and/or production ratios for possible isomer corrections should be investigated via post-trap spectroscopy. In many cases, simple half-life measurements based on β particles would enlighten the situation a lot. In summary, there is a wealth of fascinating experiments on neutron-deficient nuclei of astrophysical interest to be performed with JYFLTRAP in future.