Mass Measurements of Neutron-Deficient Y, Zr, and Nb Isotopes and Their Impact on $rp$ and $\nu p$ Nucleosynthesis Processes

Using isochronous mass spectrometry at the experimental storage ring CSRe in Lanzhou, the masses of $^{82}$Zr and $^{84}$Nb were measured for the first time with an uncertainty of $\sim 10$ keV, and the masses of $^{79}$Y, $^{81}$Zr, and $^{83}$Nb were re-determined with a higher precision. %The latter differ significantly from their literature values. The latter are significantly less bound than their literature values. Our new and accurate masses remove the irregularities of the mass surface in this region of the nuclear chart. Our results do not support the predicted island of pronounced low $\alpha$ separation energies for neutron-deficient Mo and Tc isotopes, making the formation of Zr-Nb cycle in the $rp$-process unlikely. The new proton separation energy of $^{83}$Nb was determined to be 490(400)~keV smaller than that in the Atomic Mass Evaluation 2012. This partly removes the overproduction of the $p$-nucleus $^{84}$Sr relative to the neutron-deficient molybdenum isotopes in the previous $\nu p$-process simulations.


Introduction
Stellar nucleosynthesis, especially of heavy nuclei, is of great interest in nuclear astrophysics [1,2]. There are two wellknown scenarios for producing almost all heavy chemical elements beyond Fe called s-process [2,3] and r-process [2,4].
Recently, a possibility of a synthesis in the Type Ia supernovae was also reported [11]. Specifically, we concentrate here on the study of possible contributions of the rp-process and ν pprocess for the light p-nuclei around A ∼ 90 − 100, including 92,94 Mo and 84 Sr [8][9][10]12]. Here, 84 Sr is also considered to be anomalously abundant p-nuclide [13], as the absolute abundance is comparable to those of 92,94 Mo.
The astrophysical rp- [7] and ν p- [8][9][10] processes have been suggested [14,15] to describe the production of light pnuclei. The former is related to type I X-ray bursts which occur on the surface of neutron stars accreting H-and He-rich matter from a companion star in a stellar binary system. The bursts appear periodically in hours or days corresponding to the matter-accumulation time and last for tens to hundreds of seconds. During this time neutron-deficient nuclei up to the Sn region [15,16] can be synthesized via a sequence of proton captures and β + decays. Although there is still a debate on the contribution of type I X-ray bursts to the galactic element abundances [17], such scenarios can not be totally excluded. The ν p-process is considered to occur in the inner ejecta of corecollapse supernovae which last for less than 10 s [8][9][10]. Here, slow β + decays of the waiting point nuclei are replaced by fast (n, p) reactions, where neutrons are produced in reactions of electron anti-neutrinos in the neutrino winds with free protons in the ejecta. The νp-process can produce light p-nuclei up to A ∼ 110 including 92,94 Mo, 96,98 Ru, and 84 Sr [8][9][10]. All the ν p-process simulations predict quite high production of 84 Sr, which might be due to insufficiently known nuclear data and/or ν p-process scenarios.
Although both, rp-and ν p-, processes are sensitive to the physical conditions of the stellar environments [13,18], nuclear physics parameters, especially the atomic masses of nuclides along the reaction paths, play a crucial role [13,[19][20][21]. On the one hand, rp-process model calculations based on the finite range droplet mass model 1992 (FRDM ′ 92) [22] predicted the formation of a Zr-Nb cycle [14]. The latter has been emphasized recently based on the previous experimental mass values because it would impose an upper temperature limit for the synthesis of elements beyond Nb [23]. On the other hand, the production of light p-nuclei in the ν p-process relies on unknown or highly uncertain masses in the A = 79 − 84 region. In particular precise masses [24][25][26][27] of nuclei along the path are important to explain the observed solar abundances of 92 Mo and 94 Mo [24,25]. By taking the data from the 2003 Atomic Mass Evaluation (AME ′ 03) [28], it has already been shown that masses of 82 Zr and 83 Nb are crucial for the production of 84 Sr [8,13]. Learning about the contribution of the ν p-process to 84 Sr can be decisive in understanding the origin of the most mysterious p-nuclei 92,94 Mo [13].
In this Letter, we report on precision mass measurements of five nuclei around A∼79−84. We address the region of low αseparation energies predicted by FRDM ′ 92 in neutron-deficient Mo and Tc isotopes and conclude on an impossible existence of the Zr-Nb cycle in the rp-process. Furthermore, we discuss the overproduction of 84 Sr in the νp-process.

Experiment
The experiment was conducted at the HIRFL-CSR accelerator complex [29,30] in the Institute of Modern Physics in Lanzhou. It was done in a similar way to our previous measurements described in Refs. [31][32][33]. Therefore only a brief description and specific details are given here.
A 400 MeV/u 112 Sn 35+ primary beam of about 8 × 10 7 particles per spill was delivered by the heavy-ion synchrotron CSRm and focused upon a ∼10 mm 9 Be target placed at the entrance of the fragment separator RIBLL2. The reaction products from projectile fragmentation of 112 Sn emerged from the target mainly as bare ions. They were analyzed in flight [34] by RIBLL2. A cocktail beam including the ions of interest was then injected into the experimental storage ring CSRe. The RIBLL2-CSRe were set to Bρ = 5.3347 Tm corresponding to the maximum transmission for 101 In. The CSRe was tuned into the isochronous ion-optical mode with the transition point set to γ t = 1.302. In this mode the revolution times of the ions depend in first order only on their mass-to-charge ratios [35][36][37][38].
A dedicated timing detector [39] was installed inside the CSRe aperture. It was equipped with a 19 µg/cm 2 carbon foil of 40 mm in diameter. Each time when an ion passed through the foil, secondary electrons were released from the foil surface. The electrons were transmitted isochronously by perpendicularly arranged electric and magnetic fields to a micro-channel plate (MCP) counter. The signals from the MCP were guided without amplification directly to a fast digital oscilloscope. The detection efficiency of the detector varied from about 20% to 80% depending on the overall number of stored ions and their charge. For each injection, a measurement time of 200 µs, triggered by the CSRe injection kicker, was set corresponding to about 300 revolutions of the ions in the CSRe.
Considered in the analysis were the ions which satisfied two requirements simultaneously: (1) at least 40 time signals were recorded for each ion and (2) the ion should circulate in the ring for more than 50 µs. The revolution time spectrum was obtained from all injections analogously to our previous analyses, details of which can be found in Refs. [31][32][33]. Fig. 1(a) shows a part of the spectrum zoomed on a time window of 662.7 ns ≤ t ≤ 669.9 ns. From this spectrum, the average revolution time, T , and its standard deviation, σ T , for each ion have been extracted. Most of the measured nuclides have masses known with high precision. We used N c = 28 nuclides with well-known mass values for mass calibration ( Fig. 1(b)). A third order polynomial function of mass-to-charge ratio versus T was used for the calibration. The obtained results are listed in Table 1. Since our new experimental data were included as private communications into the latest AME ′ 16 [40], for comparison we use AME ′ 12 [41].

Data analysis and results
We have re-determined the masses of each of the N c nuclides using the other N c − 1 ones as references. The differences between the re-determined mass excesses (ME) and the literature  The nuclides of interest are indicated with red letters; the peaks with possible isomer mixture not resolved in this work are shown with blue letters. Bottom: Differences between the re-determined mass excess values from this work (ME exp ) and those from AME ′ 12 [41]. Note that each of the ME exp values in Fig. 1(b) is re-determined by using the other 27 references, while the ME exp values in Fig. 1(c) are determined by using all 28 nuclides for mass calibration (see text for details). The grey shadows represent the 1σ errors from AME ′ 12.
ones [41] are compared in the Fig. 1(b). The normalized χ n defined as is calculated with n f = N c being the number of degrees of freedom. The calculated χ n = 0.90 is within the expected range of χ n = 1 ± 1/ 2n f = 1 ± 0.13 at 1σ confidence level, indicating that no additional systematic errors have to be considered. Our measurements yield the ME values of 82 Zr and 84 Nb for the first time, within an uncertainty of as low as 10 ∼ 12 keV. The masses of 81 Zr and 83 Nb are obtained to be 876(185) keV and 797(341) keV, respectively, larger than in the AME ′ 12 [41]. We note that the previous ME values for 81 Zr as well as 85 Mo are both inferred from the measurements of β -delayed proton emissions [42]. In the case of 85 Mo, a recent SHIPTRAP experiment [23] has shown that it is 1.59 MeV less bound than the literature value [42]. We now show that also 81 Zr is by ∼ 1 MeV less bound than the one from the same work [42]. Similarly, the masses of 83 Nb and 85 Nb were previously obtained from the β -endpoint measurements [43]. Both nuclei are found to be significantly less bound in a JYFLTRAP experiment ( 85 Nb, by 877 keV) [44] and in this work ( 83 Nb, by 797 keV). Fig. 2 shows two-proton (S 2p ) and two-neutron (S 2n ) separation energies for the neutron deficient isotopes in the A = 80 mass region. If our new mass values are used, the systematic trends of S 2p and S 2n become much smoother. In particular, the striking irregularities in S 2n for 81 Y, 83 Zr and 85 Nb (see the lower panel of Fig. 2) are removed. Using the systematics of S 2p , S 2n , as well as S p and S n , the masses of 78 Y, 80 Zr, 82 Nb and 84 Mo are extrapolated and averaged as given in Table 1. Details of this analysis will be presented in a forthcoming article.
The deviations of the re-determined MEs for 43 Sc, 80 Y, and 72 Br are due to the known isomers [41] at 151-keV, 228-keV, and 100-keV excitation energies, respectively. Isomeric states have been suggested in 88 Tc [45,46] and 92 Rh [47]. Our mass value for 88 Tc agrees well with the result from JYFLTRAP [25]. We note, that the widths of the revolution time peaks of 88 Tc and 92 Rh follow the systematics. This can indicate that either only one state is mainly produced in the employed nuclear reaction or the excitation energies of these isomers are very small. We also note, that Ref. [48] did not observe the population of the isomeric state in 92 Rh in fragmentation reaction.
The determined ME value for 90 Ru is by 73(25) keV more bound compared to the precise value in the literature [41] obtained from three independent penning trap measurements [25,27]. The reason for this discrepancy is unknown and needs further investigation. Using 90 Ru as a calibrant does not affect the results listed in Table 1. Table 1: One standard deviation of the revolution times (σ T ), counts, the mass excess (ME) values and proton separation energies (S p ) based on this work (IMS) and AME ′ 12 [41]. The differences (ME IMS -ME AME ′ 12 and S pIMS −S pAME ′ 12 ) are also listed. The symbol "#" indicates the one from at least one extrapolated values.

rp-process
Our new results question the pronounced island of low α separation energies (S α ) in neutron-deficient Mo isotopes, which was predicted by FRDM ′ 92 [22]. However such low S α value at 84 Mo was not supported by, e.g., the FRDM ′ 12 [49] and WS4 [50] mass models, though they also show a minimum in the alpha separation energies. Figure 3 depicts the experimental and theoretical S α values for Mo isotopes. The S α values of 85 Mo and 86 Mo in AME ′ 12 follow the predictions of FRDM ′ 92 if the previously known experimental mass of 81 Zr and the extrapolated one of 82 Zr [41,42] are used. A sudden drop of S α at 85 Mo was called to be the first evidence of the pronounced low-S α island [23]. However, if our accurate masses of 81,82 Zr are used, S α decreases smoothly with A down to 85 Mo and no sudden drop of S α at 85 Mo is observed. It is also the case for Tc isotopes, for which the reported sudden decrease of S α at 87 Tc [23] is now removed due to our new mass of 83 Nb. Fig. 3 shows that the new experimental S α data can be well described by the latest version of FRDM ′ 12 [49] and WS4 [50] mass models. The latter has been found to be the most accurate model in various mass regions [51,52]. We note, that the extrapolated S α ( 84 Mo) agrees well with the prediction by the WS4 model. The facts above indicate that the claimed pronounced low-S α island in neutron-deficient Mo isotopes does not exist.
The non-existence of the low-S α island in neutron-deficient Mo isotopes questions the formation of the predicted Zr-Nb cycle in the rp-process of type I X-ray bursts [14]. Such Zr-Nb cycle is characterized by large 84 Mo(γ, α) 80 Zr and 83 Nb(p, α) 80 Zr reaction rates, which sensitively depend on S α ( 84 Mo), i.e., the mass difference between 84 Mo and 80 Zr. Based on our extrapolated masses of 84 Mo and 80 Zr, we obtain S α ( 84 Mo) = 2.21(35) # MeV. This value agrees with the previous extrapolations but is somewhat higher than the values used in the previous type I X-ray burst model calculations in Refs. [14,23]. Furthermore, it indicates that the expected large 84 Mo(γ, α) 80 Zr and 83 Nb(p, α) 80 Zr reaction rates could significantly be reduced, leading to a weakening or even disappearance of the Zr-Nb cycle in the rp-process in type I X-ray bursts.
Network calculations [53] based on the type I X-ray burst model of Schatz et al. [15] have been performed using the new reaction rates obtained with the Talys code [54,55]. We de-   Calculations show that if our new results are used, the reaction rates favoring the formation of the Zr-Nb cycle are reduced by orders of magnitude. Fig. 4 shows the cycle branching ratio as a function of burst time for a typical burst [15]. Under the favorable conditions we assume the 1σ upper or lower limits of mass uncertainties which give the largest Q-value for the 83 Nb(p, α) 80 Zr reaction and the smallest α separation energy of 84 Mo. If the favorable masses from AME ′ 12 are used (black solid line in Fig. 4), a large branching ratio can be found at the peak temperature of ∼1.9 GK, which is the same result as obtained in Ref. [23]. The branching ratio is reduced quickly as the temperature decreases to below 1.4 GK. However, if our new masses are taken, the branching ratio into the Zr-Nb cycle is decreased, as demonstrated by the red line in Fig. 4, by several orders of magnitude even at the peak temperature of ∼1.9 GK.
Until recently it has been assumed that at high temperatures (above 2 GK) the rp-process flow stalls at the 56 Ni waiting point. However, with the new mass measurement of 56 Cu [57] there might be some flow bypassing the 56 Ni waiting point. Furthermore, there might be a possibility of an rp-process environment with seed nuclei beyond 56 Ni or with slowly rising temperature to make the flow pass through 56 Ni before reaching high temperatures. In such cases, the Zr-Nb cycle may have been relevant as a further hindrance until temperatures declined down to 1.7 GK. Our new results with certainty remove this barrier.

νp-process
In order to examine the effect of the new masses on the νpprocess, we used a semi-analytic neutrino-driven wind model and the reaction network code to obtain the thermodynamic trajectories of neutrino-driven outflows and productions of νpprocess. More details can be found in Ref. [13]. The parameters of the wind model are the "standard" ones which represent typical supernova conditions. Our calculations show that the new masses mainly affect the mass fractions in the mass region of A = 76 ∼ 86. In Fig. 5 we show the resulting abundances for the p-nuclei in this mass region. We normalize the results to the abundance of 94 Mo and compare to the solar system abundances [56] shown as filled black circles. The new masses affect neither 92 Mo nor 94 Mo. Even though in our calculation 92 Mo is a little bit more abundant than 94 Mo, it is not sufficient to explain the observed solar 92 Mo/ 94 Mo abundance ratio, which requires another mechanism as suggested by Wanajo [9], Fisker [26], and Travaglio [11]. However, the new masses have considerable effects on the production of p-nuclei 78 Kr and 84 Sr. 78 Sr is the progenitor of 78 Kr. Obviously, the production of 78 Sr is affected by the extrapolated masses of neighboring 78 Y and 80 Zr and by the measured mass of 79 Y. The relative abundance of 78 Kr is slightly increased in the calculations if our new results are taken into account. Thus the overproduction of 78 Kr relative to 94 Mo became even stronger. This result calls for  [56] and νp-process calculations based on the mass values from AME ′ 12 (AME12), our new mass values (Exp16) and our extrapolated mass values (Ext). Note that all the calculated abundances are normalized to 94 Mo further precision mass measurements of the neighboring N=Z nuclides. Also, it gives support for the reconsideration of the significant νp-process contribution to 94 Mo abundance as suggested by Wanajo [13].
Furthermore, the abundance of 84 Sr, which appears overproduced with respect to the Mo isotopes in previous calculations, is reduced. This change, which is largely related to the decrease by ∼500 keV of the proton separation energy of 83 Nb, modifies the reaction flow from 82 Zr(p, γ) 83 Nb(p, γ) 84 Mo to 82 Zr(p, γ) 83 Nb(n, p) 83 Zr(p, γ) 84 Nb. Hence, 84 Nb becomes the progenitor of 84 Sr if the new masses are used instead of 84 Mo if the masses from the AME ′ 12 are considered. This change alone will lead to a substantial decrease in the production of 84 Sr. However, it is partly compensated by the increase in the proton separation energy of 82 Nb. The latter allows for the reaction sequence 81 Zr(p, γ) 82 Nb(n, p) 82 Zr feeding into the reaction chain described above. The proton separation energy of 82 Nb is based on the extrapolation. It is rather close to the value defining the ν p-process path assuming (p, γ) ⇄ (γ, p) equilibrium, which is about 1.65 MeV for the conditions considered here. An experimental mass for 82 Nb would thus be highly welcome.

Summary
In summary, the masses of five neutron-deficient nuclei, 79 Y, 81,82 Zr, and 83,84 Nb have been precisely measured using isochronous mass spectrometry at HIRFL-CSR. Our new mass values do not support the existence of a pronounced low-S α island in Mo isotopes. As a consequence, the predicted Zr-Nb cycle in the rp-process of type I X-ray bursts does not exist or at least is much weaker than previously expected. Furthermore, our new data allowed for elimination of some uncertainties in the νp-process induced by the poorly-known nuclear masses. Based on our new mass values, the abundance estimation of the νp-process to the p-nuclides in the A∼90 region lies now on a more solid basis in terms of masses, although there are other yet unknown physical parameters, such as (n, p) reaction rates. Particularly, the new masses lead to a reduction of the