Edinburgh Research Explorer Proton decay of 108I and its significance for the termination of the astrophysical rp-process

Employing the Argonne Fragment Mass Analyzer and the implantation-decay-decay correlation technique, a weak 0.50(21)% proton decay branch was identiﬁed in 108 I for the ﬁrst time. The 108 I proton-decay width is consistent with a hindered l = 2 emission, suggesting a d 5 / 2 origin. Using the extracted 108 I proton-decay Q value of 597(13) keV, and the Q α values of the 108 I and 107 Te isotopes, a proton-decay Q value of 510(20) keV for 104 Sb was deduced. Similarly to the 112 , 113 Cs proton-emitter pair, the Q p ( 108 I) value is lower than that for the less-exotic neighbor 109 I, possibly due to enhanced proton-neutron interactions in N ≈ Z nuclei. In contrast, the present Q p ( 104 Sb) is higher than that of 105 Sb, suggesting a weaker interaction energy. For the present Q p ( 104 Sb) value, network calculations with the one-zone X-ray burst model [Phys. Rev. Lett. 98 , 212501 (2007)] predict no signiﬁcant branching into the Sn-Sb-Te cycle at 103 Sn.


Introduction
Nuclear structure and binding energies of exotic, neutron-deficient nuclei can be extracted from their α-and proton-decay properties. Far from the valley of β stability, where experiments are particularly challenging, due to 5 low production cross sections, this is often the only method available. The region in the vicinity of the N = Z line, Figure 1: The nuclear chart in the proximity of 100 Sn. A nucleus is marked as an α emitter, if it has an α-decay branch greater than 5%. The proton and α decays relevant for this work are indicated with black and green arrows, respectively. Decays observed in earlier experiments are indicated with solid lines, whereas those studied in this work are marked with dashed lines.
with the tellurium isotopes. Proton separation energies (S p = −Q p ) of antimony isotopes determine the breakout path. It has been suggested that the rp-process terminates in a Sn-Sb-Te cycle, proceeding through 106 Sb [22]. Later, based on precise mass measurements [23], it was concluded 35 that only 3% of the total flow proceeds through 106 Sb, and that a stronger branch of 13% can be expected to proceed via 107 Sb. In terms of proton separation energy, 108 Sb is an even better candidate as a potential gateway nucleus, but this branch is suppressed by the long, 115 s [24], β-40 decay half-life of 106 Sn. Furthermore, in another α-decay study [18], it was shown that the Sn-Sb-Te cycle cannot proceed through 105 Sb. However, it has been speculated [18,19] that it is possible for the cycle to flow via 104 Sb, if this nucleus is more proton-bound than expected due 45 to enhanced proton-neutron interactions [25], similarly to 112 Cs.
To date, it is not certain whether the Sn-Sb-Te cycle proceeds through 104 Sb. To address this question, the proton separation energy of 104 Sb needs to be determined.

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Due to low production cross sections, precise mass measurements, as well as direct reaction rate studies, are beyond the reach of current experimental techniques. In addition, the expected proton decay branch of 104 Sb is below 1% [26], which makes the direct observation of this pro-55 ton decay difficult. However, as the Q α values of 108 I and 107 Te are known, this can be done indirectly by measuring the Q p value of 108 I, and using energy conservation Q p ( 104 Sb) = Q α ( 107 Te) + Q p ( 108 I) − Q α ( 108 I) , see Fig.  1 for visualization. Multiple attempts to identify a pro-60 ton emission branch in 108 I have been undertaken [27][28][29], but without success. Here, we report the first observation of proton emission from 108 I. From the measured Q p ( 108 I) value, Q p ( 104 Sb) is deduced. The implications for the termination of the rp-process are addressed. In addition, more precise properties of the 108 I, 107 Te, and 112 Cs nuclei are reported.

Experimental details
The neutron-deficient nuclei of interest were produced using the 54 Fe( 58 Ni,p3n) 108 I fusion-evaporation reaction.

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The fusion-evaporation residues (referred to as recoils hereafter) were separated from the primary beam with the Fragment Mass Analyzer (FMA) [30]. The 58 Ni beam, delivered by the ATLAS facility of Argonne National Laboratory, had an average intensity of 30 pnA and an energy of 75 254 MeV. The total irradiation time of the self-supporting, 450-µg /cm 2 thick 54 Fe targets was approximately 155 hours. The high beam intensity was accommodated by mounting the targets on a rotating wheel. A 20-µg /cm 2 thick stationary carbon charge-state reset foil was placed down-80 stream from the target wheel. The FMA was set to collect recoils with A = 108 and +26 and +27 charge states. Some 107 Te and 109 I recoils were collected as a side product due to partially overlapping mass-to-charge-state ratios, which were measured at the FMA focal plane with a 85 position-sensitive parallel-grid avalanche counter (PGAC). After passing through PGAC, the recoils were implanted into a 64 mm × 64 mm, 100-µm thick, 160 × 160 strip double-sided silicon strip detector (DSSD). The gain parameter of a linear energy calibration was obtained for 90 the DSSD by using an α-calibration source containing the 240 Pu and 244 Cm isotopes. The offset parameter was obtained separately for protons and α particles from the observed activities of 109 I (Q p = 820(4) keV [31]) and 108 Te (E α = 3314(4) keV [32]). The data from all channels were 95 recorded independently, and each event was time-stamped with a 100 MHz clock. An approximately 4-µs long waveform was collected for each DSSD event in order to analyze pile-up events.
The identification of the decay events of interest was 100 based on the search for consecutive recoil implantationdecay (R-d1 ) or recoil implantation-decay-decay (R-d1-d2 ) event chains in the same pixel of the DSSD. An event was considered as a recoil implantation if the PGAC yielded a horizontal position corresponding to mass number 108, 105 the energy registered in the DSSD was greater than 15 MeV, and a time-of-flight condition between the PGAC and the DSSD was satisfied. An event without a PGAC signal was considered as a decay event, which may correspond to a proton decay, an α-particle emission, or a β + 110 decay. Because the DSSD was rather thin, β + particles were likely to punch through, resulting in a low-energy background.

Results
The energy spectrum of decay events for all observed 115 R-d1 chains is displayed in Fig. 2. The energy deposited in the DSSD by α decay of 108 I and 107 Te, once corrected for the α-decay recoil effect [33,34], yielded respective Q α is needed to account for partially overlapping α-particle energies of the nuclei of interest. Figure 4 contains the energy-energy matrix for the two 130 consecutive decay events in the observed R-d1-d2 event chains, where d1 and d2 decay times were limited to 130 ms and 18 ms, i.e., approximately 5 times the half-lives of 108 I and 107 Te, respectively. In Fig. 4, a group of eight events are temporally and spatially (same pixel of 135 the DSSD) correlated with the known α-decay of 107 Te, implying proton emission from 108 I. The time distribution of these eight proton-decay events is presented in Fig.  3(c), and for the subsequent α decays, in Fig. 3(d). The half-lives of these decay chains, extracted with the maxi-140 mum likelihood method [36], are similar to those obtained in Figs. 3(a) and 3(b), indicating proton and α-particle emission from the same state of 108 I. The energy peak corresponding to the 108 I proton-decay events, seen in the inset of Fig. 4, corresponds to a proton-decay Q value of 145 597(13) keV. A proton-decay branch of b p = 0.50(21)% was deduced from the number of observed 108 I proton and α decays. The beta decay branch was also accounted for by comparing the present half-life of 108 I and the theoretical partial β-decay half-life of 402 ms [37]. (panels (a) and (b)) or maximum likelihood method [36] (panels (c) and (d)). The solid lines in (a) and (b) are fits to the data, and the dashed lines in (c) and (d) are the probability density distributions [35] corresponding to the half-lives obtained from these fits. The peak labeled "Bgr" corresponds to random correlations, see text for details. Figure 4: Energy-energy correlation matrix for two subsequent decay events in R-d1-d2 chains, when the R-d1 and d1-d2 time differences are less than 130 ms and 18 ms, respectively. The inset provides the energy spectrum of the newly observed 108 I proton decay events, which are highlighted with a dashed circle in the main panel. Due to a high count rate in the DSSD and the long half-life, 108 Te α-decay events self-correlate randomly. The dashed lines mark the energies of selected, previously identified, charged-particle decay activities in this region.

Discussion
The results obtained in this study are summarized in Table 1 and compared to those reported in the literature. These results are discussed in detail below.

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The presently obtained Q p value of 597(13) keV for 108 I is in good agreement with the value of 600(110) keV reported in the recent mass evaluation of Ref. [31], as well as with an upper and lower limits of 600 [26] and 240 keV [19] set in earlier studies of 108 I. Given the calculated de-160 formation, β 2 = 0.15 [41], and the odd-odd character of 108 I, it is difficult to propose a firm configuration assignment for the proton decaying state. In the spherical shell model, the 1d5 /2 and 2g7 /2 orbitals are close to the Fermi surface for both protons and neutrons, indicating a high 165 level density at low excitation energies. A WKB integral predicts partial proton-decay half-lives of approximately 150 ms or 70 s for a Q p = 597 keV proton emitted with an orbital angular momentum of l = 2 or l = 4, respectively. A measured partial proton-decay half-life of 5.3(22) s was 170 deduced for 108 I from the present half-life and branching ratio. The fact that the experimental value is between the two theoretical values, suggests that the proton is emitted with l = 2 from a state which is a strong admixture of 1d5 /2 and 2g7 /2 orbitals. For comparison, the WKB in- The proton-decay half-life of neighboring 109 I was cal-180 culated recently using the nonadiabatic quasiparticle approach as a function of deformation [17]. It was concluded that the experimental half-life is consistent with a deformation of β 2 ≈ 0.15 and asymmetry of γ ≈ 15°, and that the emission proceeds from a 3 /2 + state. This level 185 was suggested to originate from a mixing of the Ω π = 1 /2 + , 3 /2 + Nilsson states, which are of 2g7 /2 and 1d5 /2 spherical parentage, respectively. It is expected that the deformation in 108 I is similar to that of 109 I [41]. However, in 108 I, the odd proton has to be coupled to the odd neu-190 tron, similarly to the case of 130 Eu [21]. The Gallagher-Moszkowski rule [42], applied to a proton and neutron occupying any combination of the 1 /2 + [431] or 3 /2 + [411] Nilsson orbitals, suggests a preferred coupling to a spin and parity of 1 + or 3 + . Since the 107 Te ground state is 195 expected to have a spin of 5 /2 + , the l = 2 proton emission from these orbitals is allowed, and would dominate over the l = 4 component. In order to quantitatively interpret proton emission from 108 I, calculations using an approach similar to that of Ref. [17], but with the inclusion of the 200 odd neutron [21], need to be performed.

Proton-decay properties of 104 Sb, and their effect on
the astrophysical rp-process Using the newly measured Q p ( 108 I) = 597(13) keV and Q α ( 108 I) = 4097(10) keV values, together with the 205 adopted Q α ( 107 Te) = 4008(5) keV [31], one can deduce a value of Q p ( 104 Sb) = 510(20) keV. This is to be compared with the Q p ( 104 Sb) = 510(100) keV, reported in the recent mass evaluation of Ref. [31], and a range of 150-520 keV estimated in Ref. [19]. A more precise value of -59.17 (8) 210 MeV for the mass excess ∆ of 104 Sb can be obtained by using the present Q p ( 104 Sb) value and ∆( 103 Sn) from Ref. [31]. In Fig. 5, the Q p values obtained in this study are compared to those of the nearby odd-Z nuclei, as well as to the predictions of selected nuclear-mass models  Zeldes [43], FRDM [41], and KTUY05 [44]). Similarly to the 112,113 Cs pair, the odd-odd 108 I has a lower Q p value than the less exotic, odd-even neighbor 109 I. This is most likely due to the residual proton-neutron interactions between the odd proton and neutron [25]. In contrast, Q p 220 for odd-odd 104 Sb is higher than that of 105 Sb, possibly due to fewer proton-neutron pairs than in the iodine and cesium nuclei. It is noteworthy that none of the mass models predicts this Q p decrease for the 112,113 Cs and 108,109 I pairs. Only the semiempirical shell-model formula of Liran 225 and Zeldes [43] anticipates such a behavior, but not until at the N = Z line. All nuclear mass models appear to systematically overestimate the Q p of antimony isotopes, but perform better for iodine and cesium nuclei. Liran-Zeldes model fits the data best on average, but it deviates 230 for 108 I and 112 Cs. The KTUY05 model [44] performs the best for nuclei beyond the proton dripline. A pico-second scale (l = 2) or nano-second scale (l = 4) half-life is expected due to high Q p value for the thus far unknown proton emitting isotopes of 103 Sb, 107 I, and 111 Cs. Given that a typical time-of-flight through a recoil separator is 1 µs, the observation of these isotopes will be very difficult.
The Sn-Sb-Te cycle branching (see Fig. 4 in Ref. [18]), obtained using network calculations with a one-zone X-ray burst model [22], indicate clearly that, with the present 240 Q p ( A Sb) value, there is no significant branching into the cycle via 104 Sb. Hence, the discussion in Ref.
[23] about the termination and final composition of the burst ashes of the astrophysical rp-process remains intact. However, these conclusions rely on the assumption that excited states 245 do not play a role in the extraction of Q p ( 104 Sb). Based on the present half-life analysis (see Fig. 3) protons and α particles are emitted from the same state of 108 I. Furthermore, the 107 Te α-decay fine structure was characterized in Ref. [45], and the Q α ( 107 Te) = 4008(5) keV corre-250 sponds to a ground state-to-ground state α decay. Therefore, the only scenario that cannot be excluded here, and that would decrease the present Q p ( 104 Sb), is if the 108 I α decay leads to an excited state of 104 Sb. Such an excited state should have an energy greater than 1 MeV in 255 order to allow a considerable branching into the Sn-Sb-Te cycle, which is unlikely. On the other hand, even a small change in Q p ( 104 Sb) would have an impact on the proton-decay branch of 104 Sb. Assuming a proton emission from the spherical 1d5 /2 orbital and the present Q p ( 104 Sb) 260 value, a WKB approximation predicts a partial protondecay half-life of approximately 4 s for 104 Sb. By comparing this to the measured half-life of 104 Sb (440 +150 −110 ms [46]), a proton-decay branch of approximately 10% can be expected. However, proton decay events following the α 265 decay of 108 I were not observed in the present experiment, limiting the proton-decay branch to 0.3% for 104 Sb, in fair agreement with the limit of 1% reported in Ref. [26]. This could occur if the 2g7 /2 proton orbital dominates the wave function of the 104 Sb ground state, or if the spin of 270 the ground state is greater than 5h, which would result in forbidden l = 2 proton emission. The predicted deformation of 104 Sb is relatively small, β 2 = 0.075 [41], but it might also slow down the proton emission from 104 Sb. The present Q α values for 107 Te and 108 I are in good agreement with those adopted in Ref. [31] and, together with the above improved mass excess of 104 Sb, yield an improved value of ∆( 108 I) = −52.65(8) MeV, see Table 1 for comparison with the recommended values. The present 280 half-life of T1 /2 ( 107 Te) = 3.6(2) ms is slightly longer compared to the value of 3.1(1) ms, adopted in the recent nuclear data evaluation [38]. The latter value is identical to that given in Ref. [29], but an earlier study [ Similarly to the Q p ( 104 Sb), also the Q α ( 112 Cs) can be calculated via energy conservation as shown in Fig. 1. With the present Q p ( 108 I) value, and with Q α ( 111 Xe) = 3723.5(100) keV [32,39] and Q p ( 112 Cs) = 816(4) keV [39], one calculates Q α ( 112 Cs) = 3940(20) keV, which is at the 295 upper limit of 3940 keV obtained in Ref. [29]. It is more precise than the adopted value of 3930(120) keV [31], and the range of 3830-4210 keV proposed in Ref. [19]. In the latter study, an upper limit of 0.26% was obtained for the 112 Cs α-decay branch. The present Q α ( 112 Cs) value 300 suggests a smaller α-decay branch of 0.07 +0.09 −0.04 % (l = 0) or 0.03 +0.04 −0.02 % (l = 2), and this possibly explains why the α decay of 112 Cs was not observed in Ref. [19]. These branches were calculated with the method of Rasmussen [47], using the reduced α-decay width of 114 Cs (δ 2 = 72 +48 −28 305 keV [19,40]), and a half-life of 506(55) µs [19] for 112 Cs.

Summary
A weak proton emission branch in 108 I was observed with a proton-decay width consistent with that of hindered l = 2 emission. In order to assign a specific config-310 uration for the proton emitting state, nonadiabatic quasiparticle calculations, similar to those presented in Refs. [17,21], are needed. Using the measured Q p ( 108 I) value, the proton-decay Q value for 104 Sb was extracted indirectly. With this value, the network calculations with 315 a one-zone X-ray burst model [18] predict no significant branching to the Sn-Sb-Te cycle via 104 Sb. Because of the enhanced residual proton-neutron interactions in N ≈ Z nuclei, the odd-odd 108 I and 112 Cs have a lower Q p values than their less-exotic odd-even neighbors 109 I and 113 Cs, 320 respectively. In contrast, the present Q p ( 104 Sb) is higher than that of 105 Sb, possibly due to fewer proton-neutron pairs in the antimony isotopes.