Electron Capture Strength for {60,62}Ni and {58,60,62,64}Ni(p,n){58,60,62,64}Cu reactions at 134.3 MeV
N. Anantaraman, Sam M. Austin, B.A. Brown, G.M. Crawley, A. Galonsky, R.G.T. Zegers, B.D. Anderson, A.R. Baldwin, B.S. Flanders, R. Madey, J.W. Watson, C.C. Foster
aa r X i v : . [ nu c l - e x ] M a y Electron Capture Strength for , Ni and , , , Ni( p, n ) , , , Cu reactions at 134.3MeV
N. Anantaraman, Sam M. Austin,
2, 3, ∗ B. A. Brown,
2, 3
G. M. Crawley,
1, 3
A. Galonsky,
1, 3
R. G. T. Zegers,
2, 3
B. D. Anderson, A. R. Baldwin, B. S. Flanders, R. Madey, J. W. Watson, and C. C. Foster National Superconducting Cyclotron LaboratoryMichigan State University, East Lansing Michigan 48824 National Superconducting Cyclotron Laboratory and Joint Institute for Nuclear Astrophysics (JINA),Michigan State University, East Lansing, MI 48824 Department of Physics and Astronomy, Michigan State University, East Lansing Michigan 48824 Department of Physics, Kent State University, Kent Ohio 44242 Indiana University Cyclotron Facility, Indiana University, Bloomington, Indiana 47405 (Dated: November 17, 2018)
Background:
The strength of electron capture for medium mass nuclei has a significant effecton the evolution of supernovae. There is insufficient knowledge of these strengths and very littledata for important radioactive nuclei.
Purpose:
Determine whether it is feasible to obtain EC strength from studies of T o + 1 excitationsin ( p, n ) reactions, and whether this might yield information for radioactive nuclei. Methods:
Cross sections for the , , , Ni( p, n ) , , , Cu reactions were measured over theangular range of 0.3 ◦ to 11.6 ◦ at 134.3 MeV using the IUCF neutron time-of-flight facility. Results:
The T o + 1 excitations in , Ni were identified by comparison with inelastic protonscattering spectra, their B (GT) were extracted, and the corresponding electron capture rates insupernovae were calculated. Data from the TRIUMF ( n, p ) experiments at 198 MeV were reanalyzed;the electron capture rates for the reanalyzed data are in moderately good agreement with the higherresolution ( p, n ) results, but differ in detail. The possibility of future measurements with radioactivenuclei was considered. Conclusions:
It is possible to determine electron capture strength from ( p, n ) experiments. Thisapproach may make it possible to obtain electron capture strength for radioactive nuclei by studying( p, n ) reactions in inverse kinematics.
PACS numbers: 25.40.Kk, 95.30.Cq
I. INTRODUCTION
Interest in allowed Gamow-Teller strength in medium-mass nuclei ( A = 20 −
70) is related to unresolved issuesconcerning weak strength in nuclear physics and astro-physics. The bulk of the electron capture (EC) strengthin nuclei is not energetically accessible to direct mea-surement, but can be obtained from charge exchange re-actions (CER): the CER cross section at low momen-tum transfer (small angles) is proportional to the GamowTeller strength B (GT) for sufficiently high bombardingenergies, above about 100-120 MeV/nucleon. The firstsystematic CER electron capture strength studies wereperformed at TRIUMF [1] using the ( n, p ) reaction at E n ≈
200 MeV and achieved a resolution of about 1MeV for a number of nuclei.Large basis shell-model calculations for these nuclei[2] are in reasonably good agreement with the ( n, p )data. There are, however, significant differences for theNi isotopes [2, 3, 4]. More recent work with higherresolution, mostly with the ( d , He) reaction [5], hasalso been in general agreement with shell model calcu- ∗ Electronic address: [email protected];URL: lations, but in some cases there are significant differ-ences even in centroid locations [6]. Data from a re-cent Ni( t , He)measurement [7] agree with the ( d , He)results [8] but less well with the TRIUMF data. The( t , He) data are in good agreement with shell model cal-culations using the KB3G two-body interaction at lowexcitation energies E x , but the agreement is poorer athigh E x . The converse is true for the GXPF1 interac-tion(for a detailed discussion see Ref. [7] and referencestherein).These uncertainties in predicted EC strength introduceuncertainties in predictions of the evolution of massivestars and the ensuing core-collapse supernovae. Theyalso affect nucleosynthesis in Type Ia supernovae and thecrust properties of neutron stars in accreting binary sys-tems. For details see Ref. [9] and references therein. Itappears that further experimental and theoretical work isnecessary to better define the effective interactions usedin shell-model calculations and to permit more reliablecalculations of electron capture strength for astrophysi-cal applications.In this paper we describe a less direct approachto studying electron capture strength: obtaining β + strength from studies of charge exchange in the β − di-rection. The strength of β − transitions to T o + 1 statesin the residual nucleus, where T o is the isospin of the tar-get nucleus, is related by an isospin geometry factor toTypeset by REVTEX FIG. 1: Diagram of transitions via ( p, n ), ( n, p ) and ( p, p ′ )interactions. More intense transitions are shown by darkerlines. With the exception of the transition to the isobaricanalog state, those shown involve transfer of total angularmomentum, spin, and isospin ∆ J = ∆ S = ∆ T = 1. Stateslabelled with the same quantum numbers are isobaric analogs.The symbols T > , T , and T < stand for T o + 1, T o and T o − + , T > states. β + strength from the same nucleus, as shown in Fig. 1.Specifically, β + /β − = ( T o + 1)(2 T o + 1). This methodhas been exploited previously for the obvious case of self-conjugate nuclei and for the T = 1 nuclei Mg [10, 11]and Ni [12, 13, 14]. Here we apply the technique tonuclei with higher isospin: , , Ni.To obtain T o + 1 strength with ( p, n ) reactions, onehas to deal with two important issues. First, the T o +1 states appear at high excitation energy, and lie on alarge background; this is presumably the reason earlierexperiments in this mass region with poorer statistics hadnot seen these states [15]. And second, charge exchangereactions such as ( p, n ) do not have an isospin meter; theyare not selective of isospin. In the present high statistics( p, n ) experiment on the T = 2 and T = 3 nuclei , Ni,we observe peaks at the expected energies of T o + 1 statesand present reasonably convincing evidence that they are T o + 1 states. It, therefore, appears that both of theabove issues can be dealt with although some ambiguitiesremain.In Section II we describe the experimental proceduresand in Section III present the results for B (GT) and re-action rates. In Section IV we discuss some options forfuture measurements of electron capture strength for ra-dioactive nuclei using inverse kinematics, with heavy ra-dioactive beams incident on hydrogenous targets. II. EXPERIMENTAL PROCEDURES
The beam-swinger time-of-flight system at the IndianaUniversity Cyclotron Facility was used to measure neu-tron time of flight spectra resulting from the bombard-ment of 36 to 50 mg/cm , , , Ni targets (isotopicallyenriched to > ◦ , 85.8 m from the target, and consisted of three identical, large volume, mean timedNE-102 detectors with a combined frontal area of 1.55m and a thickness of 10.16 cm [16]. Data were obtainedat outgoing neutron angles of 0.3, 3.9, 8.0, and 11.6 degfor several different thresholds; all thresholds gave consis-tent results to within ± et al. [17]. The over-all energy resolution was about 500 keV FWHM, worsethan usual, because of an unusual and uncorrectable jit-ter in the cyclotron timing signal. The total systematicuncertainty in the cross sections is ± T o + 1,and located near E x = 14 . Cu and Cu, respectively. The state in Cu was apparently notseen in lower statistics work on that nucleus at 120 and160 MeV [15]. A more detailed view of the T o + 1 crosssections is shown in panels (a) and (c) of Fig. 4. Theseresults show that a high statistics experiment can observethe T o + 1 states, even with relatively poor resolution. III. RESULTS
The angular distributions for the high lying excitationsin , Ni are shown in Fig. 3. The curves are DWBAcalculated shapes for L = 0 performed with the codeDWBA70 [19], effective interactions at 140 MeV fromLove and Franey [20], optical model potentials of Ref.[21], and simple ( πf / νf − / ) wave functions. The ob-served angular distributions are forward peaked and areconsistent with L = 0 GT excitations.We next deal with the evidence for assigning T o + 1as the isospin of these peaks. Perhaps most importantis the comparison with spectra for the ( p, p ′ ) reactionthat are shown on the energy axis in Fig. 2. The ( p, p ′ )reaction near zero degrees populates 1 + states preferen-tially, with a spin strength proportional to B (GT) forthe analog CER, but it can populate both isospin T o and T o + 1 states. The sharp states seen at high excitation inthe ( p, p ′ ) spectra have been assigned as T o + 1 [18, 22]for two main reasons. First, as T o of the target nucleusincreases, these states shift systematically to higher E x with respect to the T o strength, as would be expected fora state of isospin T o + 1. And second, although the statesare unbound to neutron decay and have low angular mo-mentum, they are quite narrow; their observed width isconsistent with the experimental resolution, presumablybecause the neutron decay of T o + 1 states is isospin for-bidden and the proton decay energy is well below theCoulomb barrier. The positions of the sharp ( p, p ′ ) peaksagree approximately with those seen in ( p, n ), after cor-recting for Coulomb effects, supporting a T o + 1 assign-ment for the states seen in the ( p, n ) reaction.Shell model calculations done in a simple basis [23]also support the T o + 1 assignment; the T o + 1 strength isseparated from T o strength for A >
58, and is localizedin a few strongly populated states. As expected, theseparation grows as N − Z increases. We shall see that FIG. 2: Spectra for , , , Ni ( p, n ) reactions at 134.4 MeV.There are about 10 counts per channel in these spectra, suf-ficient to observe the weak T o + 1 states as described in thetext. The numbers above the peaks in the spectra are excita-tion energies. Spectra observed in ( p, p ′ ) reactions [18] on thetarget nuclei are plotted on the energy axis. The sharp peakat the left of each ( p, p ′ ) spectrum is the lowest-lying T o + 1state. these states lie low in the spectra reached via ( n, p ) fromthe same target. A. Comparison with ( p, p ′ ) The isospin analog of a state at E x (target), seen inthe ( p, p ′ ) reaction, will occur in the ( p, n ) product nu-cleus at approximately the same energy above the ana-log of the ground state (labeled IAS in Fig. 1), i.e., E x ( p, n ) = E x ( p, p ′ ) + E x ( IAS ). In Table I the relevantenergies are tabulated, showing that the energies of theanalogs of the strongly excited ( p, p ′ ) states and of the ob-served peaks in , Cu agree within the accuracy of thepresent measurements ( ± . Cu (not visible
FIG. 3: Angular distributions for the T o + 1 excitations in Ni (upper points) and Ni (lower points). The Ni crosssections have been multiplied by 10 for display purposes. Thecurves are the DWBA calculations described in the text. on the scale of Fig. 2), but with the present resolution, itis barely one standard deviation above background, andis too weak to permit extraction of meaningful cross sec-tions. The observed widths of the lowest lying T o + 1peaks are consistent with the resolution of the ( p, n ) and( n, p ) experiments (these states are isospin forbidden todecay by neutron emission and the proton decay energyfor isospin allowed decays is in the 2 to 3 MeV range,well below the Coulomb barrier). The predicted excita-tion energies of the states in A Co that would be reachedby the corresponding A Ni( n, p ) transitions are also givenin Table I.
B. Determination of B (GT) We extracted the B (GT) corresponding to the T o + 1excitations by comparing their strength to that of theFermi (∆ L = ∆ S = 0) transition to the IAS, ( B (F) ≈ ( N − Z )), both evaluated at the same small momen-tum transfer ( q ≈ .
05 fm − ) using the standard tech-niques [25]. We make the usual assumption [25], fairlyaccurate for this energy range, that the ratio of cross sec-tions for Fermi and GT transitions of equal strength isproportional to ( E p ( M eV ) / . . This corresponds toa unit cross section, the ratio of cross section to B (GT),of 4.39 mb (4.23 mb) for Ni ( Ni), in good agreementwith the value of 4.49 mb (4.29 mb) used by [4] at 198MeV. This is not surprising since the energy dependenceof unit cross sections is weak.Determination of the number of counts in the T o + 1states in , Ni was done by fitting the data with a poly-nomial background and a sum of Gaussians. The resultsfor a quadratic background and two or three Gaussiansare shown in Fig. 4. For Ni a linear background didnot adequately reproduce the overall spectrum shape.Fits to the Ni data with three Gaussian peaks were
TABLE I: Expected and observed energies of the lowest lying T o + 1 , + states in the Cu isotopes following ( p, n ) reactions andin the Co isotopes following ( n, p ) reactions.Target E x ( A Ni) a E x (IAS) b E x ( A Cu, expected) c E x ( A Cu, observed) E x ( A Co, predicted) d E x ( A Co, observed) e (MeV) (MeV) (MeV) (MeV) (MeV) (MeV) Ni 11.85 ± ± ± Ni 14.00 ± ± ± Ni 15.62 ± a From the A Ni ( p, p ′ ) results of Refs. [18, 22] b Ref. [24] c From E x ( p, n ) = E x ( p, p ′ ) + E x ( IAS ) d Calculated from E x ( A Ni) in the first column and known Coulomb energies e From fits to the data of Ref. [4] as shown in Fig. 4. not superior within statistics, although they allowed forthe use of the same width, consistent with the energyresolution, for the three peaks. For Ni the lower lyingpeak was well defined, but the strength of a second peakcould not be determined unambiguously; its area wasfixed at the same value relative to the lower excitationpeak as in the TRIUMF data (see below). This yields asatisfactory description of the data as shown in Fig. 4.The results for B (GT) are collected in columns (2) and(3) of Table II. The uncertainties shown include a 13%systematic error, dominated by the uncertainties in thecross section of the IAS (8%) and in the extrapolation to q = 0 (10%). In most cases the statistical uncertainty islarger, because the peaks sit on a large background. The B (GT) are converted to those that would be measuredin ( n, p ) reactions by multiplying by the appropriate ra-tio of Clebsch-Gordon coefficients, 15 for Ni and 28 for Ni.
C. Comparisons with other ( p, n ) and ( n, p )data
Data for , Ni are available from 120 MeV ( p, n )measurements at IUCF [15], but the statistics are notsufficient to observe the weakly excited T o + 1 states in Ni. The 198 MeV Ni( n, p ) reaction studies at TRI-UMF observe the , , , Ni EC states directly [3, 4]and warrant a detailed comparison with the present datafor , Ni. This is not possible for , Ni. The T o + 1strength in Ni( p, n ) is not sufficiently separated from T o strength to permit a reliable identification withoutfurther information [12, 13, 14]. And as noted above thestrength we observe for Ni is significant only at the onestandard deviation level.Since only the stronger low-lying excitations can be ex-tracted from the present data, in the 6th column of TableII we compare with the results from ref. [4] as reportedin Fig. 12 of that paper, integrated over a comparableenergy range, namely up to E x = 3.2 or 4.0 MeV. Thenumbers quoted in Fig. 12 of Ref. [4] in this energy in-terval are about 25% smaller than those given in Fig. 10and Table II of that paper, as has been previously notedin Ref. [2]; we use the results in Fig. 12 because they are given as a function of excitation energy.A somewhat more detailed qualitative comparison isalso possible. Figs. 2-4 of Ref. [4], referred to as”Williams” in the following discussion, present the ( n, p )data prior to multipole decomposition. Those data aregiven in smaller bins than the final results, 300 keV com-pared to 1.0 MeV, and have structure that did not survivethe multipole decomposition procedure. For example, thespectrum for Ni in Fig. 2 of Williams has two peaksbelow E x = 4 MeV that, as is shown by their Fig. 6,are dominated by L = 0 strength. These peaks are notseparately visible in the L = 0 spectra of Williams, Fig.9. We have scanned the Williams data (in their Figs. 2and 3) for , Ni and fitted them with quadratic back-grounds and two or three Gaussians as was done for the134.3 MeV data. For the Williams Ni data, the three-Gaussian fits were superior. The quadratic backgroundspresumably account mainly for the contribution of higher L transitions, at least for the Williams data.In Fig. 4 we show both the Williams cross section dataat E n = 198 MeV and the present data for the T o + 1states at E p = 134 . Ni, the locations andspacing of the two lowest states are in excellent agree-ment; for Ni the position of the lowest lying state isthe same within about 170 keV, consistent with com-bined experimental uncertainties. The cross sections forthe lowest lying states near 0.6 MeV agree within the un-certainties. However, the relative intensities of the twolowest states for Ni observed in the present 134.3 MeVdata differ significantly from those in the Williams data.The reason for this difference is not understood. We haveinvestigated whether changes in the details of the fittingprocedure could significantly change this ratio; system-atic changes in the ratio of more than 15% seem unlikely.In order to convert the Williams cross section data ofFig. 4 to B (GT), the cross sections were extrapolatedto 0 ◦ using the Ni( n, p ) angular distribution shown inWilliams, Fig. 5, and then to q = 0 using the momen-tum transfer dependence found in the present 134.3 MeVdata. The unit cross sections from Williams were usedto convert the resulting cross sections to B (GT). The re-sults are shown in Column 4 of Table II. Only statisticalerrors, typically 3-5% are quoted in Williams. It seems TABLE II: Values of B (GT) for transitions to 1 + , T o + 1 states in A Cu: ( p, n ); and in A Co: ( n, p ). The values are those fortwo-Gaussian fits, except for the TRIUMF ( n, p ) results for Ni where the results for the three-Gaussian fits are shown inparentheses.Target( E x -MeV) a B (GT)-( p, n ) B (GT)-( n, p ) b B (GT)-( n, p ) c B (GT) sm d B (GT) TRIUMF e Ni(0.65) 0.063 ± ± Ni(2.4) 0.026 ± ± Ni(0.65+2.4) 0.089 ± ± Ni(0.6) 0.032 ± ± Ni(2.3) 0.014 ± ± Ni(0.6+2.3) 0.046 ± ± a The E x are the positions that these states would occur in the analog system Co. b Obtained by multiplying the results obtained from ( p, n ) listed in the second column by the isospin geometry factors: 15.0 for Ni, and28.0 for Ni. c From the data of Figs. 2 and 3 in Ref. [4] as analyzed in the present paper using, mainly, two-Gaussian fits. The values in parenthesesfor Ni are the results of three-Gaussian fits after summing the strengths for the upper two states; for separate values see Fig. 5. Fordetails see text. d From Caurier, et al. [2]. The strength quoted is the sum of strengths to 1 + states lying below 3.2 (4.0) MeV. e From Ref. [4], Fig. 12, integrated over the energy range up to 3.2 (4.0) MeV. probable, however, given various experimental uncertain-ties and uncertainties in the unit cross section that theoverall uncertainties are at least 10% and perhaps larger.As we have noted for the cross sections, the values of B (GT) from the ( p, n ) and ( n, p ) reactions agree withinthe uncertainties for the states near 0.6 MeV in , Ni,but the excitation of the 2.4 MeV state in Ni is muchstronger in ( n, p ). D. Comparisons with shell-model calculations
In Table II we compare our results with the large basisshell-model calculations of Ref. [2]. These calculationsuse a renormalized (reduced) GT operator, g A /g V = 1 . E x = 4 . Ni differs greatly from experiment, mainly lyingnear the high energy peak of Fig. 4.
E. Comparisons of B (GT) and electron-capturerates The values of B (GT) for Ni from the two experi-ments and from the shell model calculations of Ref. [2]are shown in Fig. 5. In cases where the fitted cross sec-tion peaks had widths consistent with the experimentalresolution we plotted their B (GT) at the position of thepeak; this applied to the lower lying peak in all the datafitted in this paper and to the higher-lying peak when fit-ted by the sum of two Gaussians. When the higher-lyingpeak was fitted by a single Gaussian, the fitted widthwas greater than the resolution, and the strength was di-vided into 200 keV bins. The values obtained are plottedin panels (a) and (b) of Fig. 5. In Fig. 12 of Williams [4]the B (GT) are given in 1.0 MeV wide bins, with one of the bins extending to E x = -0.5 MeV. The 1.0 MeV binswere subdivided into 200 keV intervals, and the values at E x < B (GT) of Fig. 5. The results from Fig. 12of Williams [4] extend to lower E x than do those fromthe analyses of the same date carried out in this paper,presumably as a result of the binning procedure used inthe multipole analysis. This will result in larger electroncapture rates at relatively low temperatures and densi-ties in astrophysical environments, as we show in Fig. 6.We would argue that the results of the present analysisare more reliable. On the other hand, the strengths pre-dicted by the shell model [2] are peaked at high energiesand will become important only at rather high tempera-tures or densities.Electron capture rates are calculated for the differentdistributions of Fig. 5 using the code described in Ref.[26]. Electron chemical potentials were computed from atabulation [27]. These calculations ignore contributionsfrom higher-lying states and from capture on thermallyexcited states that will be important at high tempera-tures and densities. Details of the calculation and addi-tional references are given in [7].Rates were calculated on a grid including values of ρY e from 10 to 10 gcm − and of T from (0.01-100) × K. In Fig. 6 we show the rates for two representative ρY e of interest in the pre-supernova evolution of massivestars: ρY e = 10 and 10 gcm − . In a 25 M sun star, forexample, the former is characteristic of various stages ofSi burning, when the temperature T ≈ −
4; the latteroccurs late in the pre-supernova stage when T > ∼ H MeV L Σ H m b (cid:144) s r - . M e V L Ni TRIUMF H d L H MeV2.52.552.62.652.7 Σ H m b (cid:144) s r - M e V L Ni PRESENT H c L H MeV L Σ H m b (cid:144) s r - M e V L Ni TRIUMF H b L H MeV L Σ H m b (cid:144) s r - M e V L Ni PRESENT H a L FIG. 4: (Color on line) Panel (a): Spectrum for Ni( p, n ) Co at 134.3 MeV, in the region of the T o +1 states.The black and gray curves are two- and three-Gaussian fits,resp. Panel (b): Spectrum for Ni( n, p ) Co at 198 MeV.The black and gray curves are two- and three-Gaussian fits,resp. Panel (c): Spectrum for Ni( p, n ) Co at 134.3 MeV,in the region of the T o + 1 states. Panel (d): Spectrum for Ni( n, p ) Co at 198 MeV. The 198 MeV data are from Ref.[4] and the 134.3 MeV data are from the present work. Spec-tra are fitted with a second order polynomial background andtwo or three Gaussian peaks. For details see the text. x ( Co) (MeV)d) B ( G T ) LSSM
FIG. 5: Values of B (GT) for Ni obtained from the present134.3 MeV ( p, n ) data and the 198 MeV TRIUMF ( n, p ) data.Panels (a) and (b) show the results of the fits to the ( p, n ) andthe ( n, p ) cross sections as described in the text and shown inFig, 4. Panel (c) shows B (GT) from the Multipole Decompo-sition Analysis (MDA) performed in Williams [4], and shownin Williams Fig. 12. The results from large scale shell modelcalculations [2] are shown in panel (d). For details see thetext. We find that: (1) The rates for the two- and three-Gaussian fits to the 134.3 MeV ( p, n ) data are almostthe same over the entire parameter space, reflecting thesimilarity of the two and three-Gaussian fits. (2) TheTRIUMF results for the Gaussian fits made in the presentpaper differ from the 134.3 MeV data, but rates for thethree-Gaussian fits are in fairly good agreement, espe-cially at the higher densities and/or temperatures. (3)At lower temperatures and densities, the rates for the B (GT) results presented in Fig. 12 of Williams [4] areconsiderably higher than the others shown.We conclude from these comments that the MultipoleDecomposition Analysis for the TRIUMF data affects theresulting B (GT)s significantly, at least for Ni. It alsoappears that obtaining electron capture rates from ( p, n ) -16-14-12-10-8-6-4-20 a) ρ Y e =10 gcm -3 l og ( λ e / s ) MSU - 2 Gaussian fitMSU - 3 Gaussian fitTRIUMF - 2 Gaussian fitTRIUMF - 3 Gaussian fitTRIUMF - MDALSSM -0.4-0.200.20.40.6 b) ρ Y e =10 gcm -3 λ e / λ e , M S U - gau ss i an s c) ρ Y e =10 gcm -3 d) ρ Y e =10 gcm -3 FIG. 6: (Color on line)Reaction rates obtained from the B (GT) of Fig. 5. The upper two panes show the absolute rates andthe lower two panels the results compared to those for the 134.3 MeV ( p, n ) data. For details see the text. data is a viable procedure. IV. MEASUREMENTS OF EC STRENGTH FORRADIOACTIVE NUCLEI.
Studies of the electron capture strength of radioactivenuclei must be done using inverse kinematics (IK), witha radioactive beam of heavy nuclei incident on a lighttarget. Such studies will be necessary to explore nucleiwith significant neutron excesses and to make possiblestudies on odd-odd nuclei; among these only V is a sta-ble target. Under the conditions of interest ( θ c.m. near0 ◦ , E x in the 0-15 MeV range) the outgoing light par-ticles typically have small energies; if these particles arecharged, exceedingly thin targets are required, yieldinga very small reaction rate. The ( p, n ) reaction does nothave this problem; the low energy neutrons can easilyleave the target.There are, however, limitations on the use of the ( p, n )technique. It is applicable only to nuclei with isospinlarge enough that the splitting of T o and T o + 1 statesallows one to isolate T o + 1 strength with reasonable cer-tainty. For a T o = 1 nucleus like Ni the T o and T o + 1excitations are strongly intermixed as discussed in de- tail in ref. [12]. Because the strength of a transition isroughly proportional to 1 /T o , the isospin must also besufficiently small that the T o + 1 states are observable. Inthe present experiment the T o + 1 states were barely seenin Ni with T o = 4. Better resolution would increasethe peak to background ratio and make it possible to ob-serve T o + 1 states for nuclei with higher isospin. If, forexample, a resolution of 200 keV could be obtained forIK ( p, n ) reactions, 2.5 times better than in the presentexperiment, one could study nuclei where the relativestrength of the T o +1 excitations is a factor of 2.5 smaller,corresponding to T o as large as 5 ( Ni has T o = 3). Itis not clear whether such nuclei can be reached in prac-tice; one may be limited by the intrinsic decay widths orspreading widths of the states. And obtaining 200 keVresolution will be challenging; it will certainly require theintensities of an advanced radioactive beam facility. Atpresent intensities feasible resolutions are in the 0.5-1.0MeV range.Inverse kinematics ( p, n ) approaches are being under-taken at the NSCL. Detecting the low energy neutrons isfeasible, but presents a significant challenge. Moreover,the c.m. energy typically depends on the laboratory an-gle of the emitted neutron so the detection system musthave high angular granularity to obtain good resolutionin E x . Construction of a detector that will meet thesechallenges is underway. V. SUMMARY
We have shown that ( p, n ) reactions at 134.3 MeV havesufficient sensitivity to extract B (GT) for strongly ex-cited T o + 1 states, provided that the isospin of the targetnucleus is neither too large nor too small. Electron cap-ture strengths for the lowest lying T o + 1 states in , Niwere extracted from data for the ( p, n ) reaction and com-pared with ( n, p ) data and with large basis shell modelpredictions. The fits to the raw TRIUMF ( n, p ) crosssection data performed in the present paper yield resultsrather close to the ( p, n ) results for the lowest lying peakbut have larger strength to higher-lying states for Ni asshown in Fig. 4. However, the multipole analysis leadingto the B (GT) presented in Williams Ref. [4] moves somestrength to lower energies.Electron capture rates were calculated for two casesof interest in the pre-supernova evolution of massive stars. The results for the present analyses of the 134.3MeV ( p, n ) data and of the Williams ( n, p ) data arein reasonable agreement, except at the lowest temper-atures and densities. However, the B (GT) extracted bythe Williams multipole analysis yields significantly largerrates, particularly at low T .That ( p, n ) reactions lead to electron capture rates thatare in agreement with ( n, p ) results, when both are ana-lyzed in the same fashion, supports using ( p, n ) reactionsin IK to study T o + 1 states in radioactive nuclei. Weconclude that the IK approach may be useful for the ra-dioactive nuclei that play an important role in supernovaevolution and whose electron capture strength is difficultto obtain in other ways. Acknowledgments
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