β-decay of ^{61}V and its Role in Cooling Accreted Neutron Star Crusts
W.-J. Ong, E. F. Brown, J. Browne, S. Ahn, K. Childers, B. P. Crider, A. C. Dombos, S. S. Gupta, G. W. Hitt, C. Langer, R. Lewis, S. N. Liddick, S. Lyons, Z. Meisel, P. Möller, F. Montes, F. Naqvi, J. Pereira, C. Prokop, D. Richman, H. Schatz, K. Schmidt, A. Spyrou
ββ -decay of V and its Role in Cooling Accreted Neutron Star Crusts
W.-J. Ong,
1, 2, 3, ∗ E. F. Brown,
2, 3, 4, 5
J. Browne,
2, 3
S. Ahn,
6, 4
K. Childers,
7, 3
B. P. Crider, A. C. Dombos,
2, 3, 4
S. S. Gupta, G. W. Hitt, C. Langer, R. Lewis,
7, 3
S. N. Liddick,
7, 3
S. Lyons,
3, 4
Z. Meisel,
12, 4
P. M¨oller,
13, 4
F. Montes,
3, 4
F. Naqvi,
3, 4, 14
J. Pereira,
3, 4
C. Prokop, D. Richman,
2, 15
H. Schatz,
2, 3, 4
K. Schmidt,
3, 4, † and A. Spyrou
2, 3, 4 Nuclear and Chemical Sciences Division, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA National Superconducting Cyclotron Laboratory, East Lansing, MI 48824, USA Joint Institute for Nuclear Astrophysics – Center for the Evolution of the Elements,Michigan State University, East Lansing, MI 48824, USA Department of Computational Mathematics, Science, and Engineering,Michigan State University, East Lansing, MI 48824, USA Cylotron Institute, Texas A & M University, College Station, TX 77843, USA Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA Department of Physics and Astronomy, Mississippi State University, Mississippi State, MS 39762, USA Indian Institute of Technology Ropar, Nangal Road, Rupnagar (Ropar), Punjab 140 001, India Department of Physics and Engineering Science,Coastal Carolina University, Conway, SC 29528, USA Institute for Applied Physics, Goethe-University Frankfurt a. M., Frankfurt am Main 60438, Germany Department of Physics and Astronomy, Ohio Univeristy, Athens, OH 45701, USA Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India Los Alamos National Laboratory, Los Alamos, NM 87545, USA (Dated: January 12, 2021)The interpretation of observations of cooling neutron star crusts in quasi-persistent X-ray tran-sients is affected by predictions of the strength of neutrino cooling via crust Urca processes. Thestrength of crust Urca neutrino cooling depends sensitively on the electron-capture and β -decayground-state to ground-state transition strengths of neutron-rich rare isotopes. Nuclei with massnumber A = 61 are predicted to be among the most abundant in accreted crusts, and the lastremaining experimentally undetermined ground-state to ground-state transition strength was the β -decay of V. This work reports the first experimental determination of this transition strength,a ground-state branching of 8.1 +2 . − . %, corresponding to a log ft value of 5.5 +0 . − . . This result wasachieved through the measurement of the β -delayed γ rays using the total absorption spectrometerSuN and the measurement of the β -delayed neutron branch using the neutron long counter systemNERO at the National Superconducting Cyclotron Laboratory at Michigan State University. Thismethod helps to mitigate the impact of the Pandemonium effect in extremely neutron-rich nucleion experimental results. The result implies that A = 61 nuclei do not provide the strongest coolingin accreted neutron star crusts as expected by some predictions, but that their cooling is still largercompared to most other mass numbers. Only nuclei with mass numbers 31, 33, and 55 are predictedto be cooling more strongly. However, the theoretical predictions for the transition strengths ofthese nuclei are not consistently accurate enough to draw conclusions on crust cooling. With theexperimental approach developed in this work all relevant transitions are within reach to be studiedin the future. X-ray observations of the cooling of transiently accret-ing neutron stars provide insights into the properties ofthe star. In quasi-persistent systems where accretionturns off for years, long-term observations reveal the ther-mal profile of the crust, which probes heat capacity andheat-transport properties of dense matter (see [1] for arecent review). The crust, an outer layer where the nu-clei are arranged in a lattice, is built up from the hotashes of thermonuclear X-ray bursts that occur on thesurface of the neutron star during the accretion phase[2, 3]. These ashes are incorporated into the neutron starcrust by ongoing accretion and converted into increas-ingly neutron-rich species through electron captures thatoccur when the Fermi energy of the degenerate electrons exceeds the electron-capture energy thresholds [4–10]. Ithas been shown that under realistic crust conditions atnon-zero temperatures, the thermal elevation of electronsabove the Fermi surface allows in some cases the reverse β -decay reactions to occur in addition to the electron-capture reactions [11]. The resulting cycle of alternatingelectron captures and β decays between the same pair ofnuclei can lead to rapid neutrino cooling. If efficient, sucha crust Urca process can impact the cooling behavior ofthe neutron star and has to be taken into account wheninterpreting X-ray observations of cooling neutron stars[12, 13].Within an electron-capture sequence along an isobaricmass chain, strong Urca cooling occurs when there are a r X i v : . [ nu c l - e x ] J a n strong ground-state to ground-state electron-capture and β -decay transitions, and when the subsequent electroncapture to the A, Z − A = 31 ,
33 mass chains, due in part to their significantabundance in rp-process ashes [14]; however, the compo-sition of the burst ashes in this mass region is uncertainas it depends on freezeout conditions and residual heliumburning [15]. An important question addressed here iswhether there is any significant cooling from the ashesof the rp-process, which predominantly produces nucleiin the A = 56–72 mass range [14–16]. The theoreticalmodel to predict electron capture and β -decay transitionstrengths used in current crust models is the QRPA-fY[17, 18] owing to its ability to make consistent predictionsfor all relevant nuclei [19, 20]. QRPA-fY predicts A = 56to be the strongest cooling isobaric chain, but recent ex-perimental and theoretical results have shown that thismass chain does not in fact cool at all [21]. Based on thecomposition of the rp-process ashes, this leaves the odd A chains A = 55 , , , , ,
65 (the most abundant odd-A ashes) as predicted candidates for Urca cooling tran-sitions. In order to ascertain whether the most commonaccreted neutron star crusts from mixed H/He bursts ex-hibit significant crust Urca cooling, and to quantify theneutrino cooling rates, it is important to experimentallyconstrain the ground-state to ground-state transitions inthese mass chains. We present here an experimental ap-proach to provide such constraints, and apply it to the A = 61 mass chain for the first time.Of all the relevant odd-A nuclides in X-ray burst ashes, A = 61 nuclei are second most abundant (after A = 65).It has also been shown that within the uncertainty ofthe Ga(p, γ ) Ge reaction rate in X-ray burst mod-els, A = 61 could even be the most dominant con-stituent in the rp-process ash [14]. Of the four rele-vant electron-capture transitions in this mass chain thatare located in the outer crust, experiments in the β de-cay direction have established ground-state to ground-state transitions for the first three, with strengths oflog f t β ( Fe) ≥ f t β ( Mn) = 5.02(3) [23],and log f t β ( Cr) = 5.1(2) [24]. Given these transi-tion strengths and the smaller electron-capture Q -values,Urca cooling in the A = 61 chain occurs, but is relativelyweak. However, for the fourth electron capture from Crto V, an allowed ground-state to ground-state tran-sition is also possible when considering selection rulesand the estimated ground-state spins for Cr (5 / − )and V (3 / − ). QRPA-fY theory does not predict aground-state to ground-state electron-capture transition(the lowest-lying transition from the ground state is pre-dicted to a state with 3 MeV excitation energy in V).However, QRPA-fY does predict a strong transition (log f t =4.35) in the β -decay direction from V to a low-lyingstate with an excitation energy of just 10 keV in Cr.Within the theoretical uncertainties this excitation en-ergy would be consistent with the ground state. If indeedthere were a strong ground-state to ground-state transi-tion with log f t =4.35, A = 61 would become the mostimportant Urca cooling chain for rp-process ashes, evenwithout a larger A = 61 abundance from a lower thanpredicted Ga(p, γ ) Ge reaction rate in X-ray bursts.In the β -decay direction, such a strong transition wouldstill be compatible with the experimentally determined48.3 ms half-life [25] within the relatively large Q-valueuncertainties of 12.0 ± >
65% ground-state to ground-state branching for thedecay.Previous β -delayed γ -spectroscopy studies of V usingan array of high-purity germanium detectors deduced anupper limit for the β -decay branch to the ground stateof Cr of 40% [27]. This corresponds to a lower limiton the log f t value of 4.6, still a very strong Urca cycle.This limit was obtained from identifying transitions to 12excited states and determining the corresponding β de-cay feeding intensities. This level scheme is incomplete,as only states up to 2.26 MeV were identified, while the β -decay Q-value is ≈
12 MeV, and it is likely that thededuced β -decay feeding intensities reported were sub-ject to the Pandemonium effect [28]. Here, we reportthe first determination of the β decay branch of Vto the ground state and use an experimental approachthat combines use of the total absorption γ -spectrometerSuN [29] and the neutron detector NERO [30]. Withits high summing efficiency, SuN is capable of detectingeven very weak γ -emitting transitions in Cr fed by the β decay of V. This avoids the Pandemonium effect andenables accurate determination of all feeding intensities.NERO was used to determine the total β -delayed neutronemission branch, including the transition to the groundstate of Cr that cannot be determined through γ -raydetection. The ground-state to ground-state branch isextracted from the total number of decays by accountingfor the β -delayed γ branchings to all exited states aboveand below the neutron separation energy in Cr and the β -delayed neutron branch to Cr measured with NERO.The experiment was performed at the National Super-conducting Cyclotron Laboratory (NSCL) at MichiganState University. V was produced as part of a mixedsecondary beam (36% V) by impinging a Se primarybeam (140 MeV/u, 35 pnA) on a 352 mg/cm Be targetand purifying the ensuing fragment beam with the A1900fragment separator [31]. The secondary beam was trans-ported to the experimental end station where it was im-planted into a double-sided Si strip detector (DSSD) ata total rate of ≈
80 pps. An Si PIN detector upstream ofthe DSSD was used to characterize incoming beam par-ticles by recording energy loss and the time of flight fromthe A1900 scintillator. Multiplicity C oun t s Energy (MeV) C oun t s / k e V FIG. 1. Experimental (black) and fitted (red) total absorptionspectrum (top), singles spectrum (bottom), and multiplicitydistribution of the detector segment (inset). The 1- σ errorband of the fit is shown in blue. The high-energy tail in thetotal absorption spectrum is due to a combination of the high-energy β particles from low-energy entry states entering SuNand γ -decay cascades from high-energy entry states. The experiment was carried out in two parts: In thefirst part ≈ V ions were implanted into a DSSDthat was part of the NSCL Beta Counting System [32]located in the center of the NERO neutron detector todetect β -delayed neutrons in coincidence with β -particlesdetected by the DSSD following an ion implantation. Inthe second part of the experiment, approximately onemillion V ions were implanted into a mini DSSD locatedat the target position of the SuN γ -ray detector to detect β -delayed γ rays in coincidence with β particles. Themeasured half-life of V was 48 ± β -delayed neutron emission P n =14.5 ± V beam particle. This is consistent with P n >
12% independently determined from the SuN data, whichcontains peaks from the γ decay of the β -delayed neutrondaughter Cr.For the SuN measurement, the energies deposited byall β -delayed γ rays emitted in coincidence with each de-tected β decay were summed together to create the totalabsorption spectrum shown in Fig. 1. The β -feeding in-tensity to each state in Cr is related to the backgroundcorrected area of the total absorption peak at the excita-tion energy of the state. The total absorption spectrumshows peaks for all previously identified states [27], butno additional isolated states were identified owing to thelimited resolution of SuN and background from summing with β -particles. Nevertheless, the total absorption spec-trum records the feeding of all additional states. To ex-tract this information we followed the analysis describedin [38, 39]. Templates of the total absorption spectra for β decays to states in Cr and β -delayed neutron emis-sion to states in Cr are generated using GEANT4 sim-ulations. In addition to transitions to individual states,transitions to unknown levels above 2.26 MeV are treatedas a quasi-continuum, with pseudolevels inserted every50 keV up to 3.2 MeV, every 100 keV up to 3.95 MeVand every 200 keV up to the Q -value of 12.0 (0.9) MeV[26], following the resolution of the SuN detector.Because the γ -ray summing efficiency is less than 100%there is a remaining dependency of the total absorptionspectrum on the detailed γ -ray cascade emitted follow-ing the β -decay feeding of a state. For the individualstates in the known level scheme, the cascade branchingswere determined using spectra of individual segments ofSuN. For the quasi-continuum states, the statistical code Dicebox [40] was used, with input parameters for thenuclear level density and γ -ray strength functions takenfrom the RIPL-3 database [41]. The measured total ab-sorption and γ -ray singles spectra were then simulta-neously fitted as a linear combination of all templates.The β -decay transition strengths, including the β -delayedneutron emission feeding, are then the normalized fit co-efficients. Fig. 1 shows the good agreement of the tem-plate fit with the measured spectrum as well as the γ -raymultiplicity distribution. The χ values per degree offreedom are 1.26, 3.53 and 1.31 for the total absorptionspectrum, the singles spectrum, and the combined data,respectively. The resulting β -feeding intensities are listedin Tab. I. The inferred feedings of low lying states from[25, 27] (right column in Tab. I) are systematically largerbecause of missed transitions from higher-lying states.The significant feeding to states above the previouslyhighest-known 2.26 MeV state inferred from our mea-surement also allows us to deduce a value, instead of anupper limit, for the feeding of the ground state.To assess the error in the β -feeding intensities ex-tracted from the fit, a Monte Carlo bootstrap study [42]was performed with 100,000 drawn samples of syntheticdata (greater than the validity sample number metric n ln( n ) ≈ χ min-imization procedure. The resultant distribution for eachof the parameters was then used to determine the error ineach parameter. Additionally, the impact of the uncer-tainty in the β -decay Q -value on the extracted β -feedingintensities was investigated by repeating the fit over therange of the uncertainty of the Q -value by varying themaximum energy of the pseudolevels included. The im-pact of Q -value uncertainties was found to be negligi-ble compared to the error from the fit, as the feeding ofthe states with the highest excitation energy is relativelyweak. Finally, the systematic uncertainty associated with TABLE I. List of β -feeding intensities from this work (leftcolumn) to the identified states in the Cr excitation schemefrom [27], and the corresponding apparent β feedings deducedby [25] from [27] (right column). The errors given here reflectboth the statistical and systematic errors.State (keV) This work (%) Suchyta et al. [25, 27] (%)0 8.1 +2 . − . < +0 . − . +0 . − .
10 (6)224 2.0 +0 . − . +0 . − . +0 . − , +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . +0 . − . +9 − - P n +3 − - uncertainties in the input parameters for Dicebox (suchas the chosen models for the γ -ray strength function orlevel density), was assessed by repeating the χ minimiza-tion procedure with new pseudolevel templates generatedwhen using different Dicebox inputs. About 50% of thefinal uncertainties are due to this systematic error.Since the f t values also depend on the Q-value throughthe Fermi integral, the Q-value uncertainty was also in-corporated into the total uncertainties in the f t val-ues using Gaussian error propagation. The Q -value un-certainty is dominated by the mass uncertainty of V(∆ M = − . ± f t uncertainties from ± ± B (GT) strengths from ourwork (assuming that all transitions are allowed) belowthe Cr neutron separation energy S n = 3 . ± . (cid:15) ≈ − . V [44].This would imply a ν [321]3/2 − ground state for Crand a π [303]5/2 − ground state for V (e.g. [45]). Previ-ous work had tentatively assigned ground-state spins andparities of 5/2 − for Cr and 3/2 − for V and explainedthese with a moderate prolate deformation [27]. Eitherscenario results in an allowed transition and is thus con-sistent with our data.QRPA-fY correctly predicts a transition to around theground state. However, this transition is to an excitedstate at 10 keV in Cr and is therefore not includedin the predicted electron-capture transitions on the Crground state. Current crust models that only considerground-state electron captures [10] therefore do not in-clude a Cr– V Urca cooling pair. This shows the im-portance of including low-lying excited parent states inelectron-capture transitions. Overall, theory predicts sig-nificant strength at low excitation energies in line withexperimental results, though the measured strength ismore spread out than predicted, resulting in less strengthnear the ground state. The strength function above theneutron separation energy is probed by the measured P n -value. Here, the predicted value from QRPA-fY of 19%is in good agreement with our measured value of 14.5 ± A = 61 nuclei in neutron star crusts solely us-ing experimental data . To determine crust cooling foraccreting neutron stars that exhibit rp-process bursts,we folded the calculated cooling rates in individual masschains with the rp-process ash abundances from [14]. Theresult is shown in Fig. 3. Our deduced ground-state toground-state log f t value of 5.5 +0 . − . from this work is sig-nificantly higher than the theory value of 4.35 predictedfor the lowest-lying transition by the QRPA-fY modeland results in an Urca cooling rate slower by a factor of14. It is consistent with the lower limit of 4.6 impliedby the 40% upper limit of the ground-state to ground-state branch from [27]. Our most important conclusion The experimentally deduced log ft values for the ground-stateto ground-state transitions in the other Urca pairs along the A = 61 mass chain may have, unlike our measurement, signifi-cant additional systematic uncertainties from the Pandemoniumeffect. The cooling contribution estimated from these other Urcapairs is therefore an upper limit. Excitation Energy in Daughter Nucleus (MeV) B ( G T ) T r a n s i t i o n S t r e n g t h ExperimentTheory
FIG. 2. B(GT) strength for the β -decay of V as functionof excitation energy in the daughter nucleus, deduced fromthe γ -ray data from this work (solid black) and predictedby QRPA-fY (red, dashed). Note that γ -ray data can onlyprovide the strength function up to the neutron separationenergy of 3.9 MeV. is that our result clearly rules out the large cooling con-tribution from A = 61 ashes predicted when employingthe QRPA-fY V β -decay log f t value for the transi-tion to the 10 keV state in Cr. Nevertheless we findthat neutrino cooling from A = 61 is significantly largerthan predicted when taking QRPA-fY ground-state toground-state transitions at face value.We also find that based on our results the Cr– VUrca pair still makes the A = 61 mass chain one of thestrongest cooling chains in accreted neutron star crusts(Fig. 3). Only A = 31 ,
33, and 55 nuclei are predictedto provide stronger neutrino cooling than A = 61. Reli-able experimental data are still lacking for ground-stateto ground-state transitions within those other isobaricchains. We note it was recently pointed out that neutrontransfer reactions may alter the distribution of abun-dances across mass chains from the initial burst ashesdistribution [47]. This may alter the relative weight ofthe individual mass chains in the ash composition. Tak-ing this effect into account would require a significantlyexpanded reaction network with detailed sets of realisticashes, which is under development but beyond the scopeof this experimental paper. Our data on the Cr- VUrca pair will be an important input in such future cal-culations.In summary we have developed an experimental ap-proach to infer β -decay ground-state to ground-statetransition strengths for neutron-rich nuclei, and demon-strated the importance of such measurements to obtainreasonably accurate data on Urca cooling in accretedneutron star crusts. The Urca cooling from A = 61 nucleican now be determined based on experimental data. Itwill be important to also investigate the strong predictedcooling in the A = 31, A = 33, and A = 55 mass chains.
20 30 40 50 60 70
Mass Number A C oo li ng ( × e r g / s ) FIG. 3. The neutrino cooling contribution from individualmass chains for a neutron star crust made from rp-processashes [14]. Predictions based on QRPA-fY (blue filled di-amonds) are shown for the strongest cooling chains. For A = 61 we also show the QRPA-fY prediction when assumingthe predicted 10 keV daughter state in Cr populated by the β -decay of V is in fact the ground state (red open square,see text for more discussion). The A = 61 cooling rates basedon experimental transition strengths are shown without thecontribution from the Cr– V Urca pair studied in this work(orange circle) and with the new data on Cr– V from thiswork (red error bar). Results shown are for a neutron starradius R = 12 km and a temperature T = 0 . R T for different physical parameters. In particular A = 55 is now the strongest predicted cool-ing mass chain within the mass range of the rp-processashes. All relevant transitions in these mass chains arewithin reach for future studies with the experimental ap-proach developed in this work.We thank M. Emeric and A. Sonzogni for creatingthe LOGFT web tool. This work was conducted withthe support of Michigan State University, the NationalScience Foundation under Grants PHY-1102511, PHY-1404442, PHY-1713857, PHY-1430152 (JINA Center forthe Evolution of the Elements), and AST-1516969. It wasadditionally supported by the Department of Energy Na-tional Nuclear Security Administration through AwardNumbers DE-NA-0003221 and DE-NA-0002132 and un-der the Nuclear Science and Security Consortium underAward Number(s) DE-NA0003180 and DE-NA0000979,and performed under the auspices of the U.S. Depart-ment of Energy by Lawrence Livermore National Lab-oratory under Contract DE-AC52-07NA27344. A. Spy-rou would like to acknowledge support under NSF careergrant PHY-1350234. ∗ [email protected] † Present Address: Institute of Radiation Physics,Helmholtz-Zentrum Dresden-Rossendorf, Dresden 01328,Germany[1] Z. Meisel, A. Deibel, L. Keek, P. Shternin, and J. Elfritz,
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