Precision measurements were carried out to test the similarities between the
ground states of 76Ge and 76Se. The extent to which these two nuclei can be
characterized as consisting of correlated pairs of neutrons in a BCS-like
ground state was studied. The pair removal (p,t) reaction was measured at the
far forward angle of 3 degrees. The relative cross sections are consistent (at
the 5% level) with the description of these nuclei in terms of a correlated
pairing state outside the N=28 closed shells with no pairing vibrations. Data
were also obtained for 74Ge and 78Se

Clark, J. A.

Deibel, C.

Freeman, S. J.

Gros, S.

Heinz, A.

Hirata, D.

Jiang, C. L.

Kay, B. P.

Parikh, A.

Parker, P. D.

Qian, J.

Rehm, K. E.

Schiffer, J. P.

Tang, X. D.

Villari, A. C. C.

Werner, V.

Wrede, C.

English

arXiv

Precision measurements were carried out to test the similarities between the ground states of 76Ge and 76Se. The extent to which these two nuclei can be characterized as consisting of correlated pairs of neutrons in a BCS-like ground state was studied. The pair removal (p,t) reaction was measured at the far forward angle of 3°. The relative cross sections are consistent (at the 5% level) with the description of these nuclei in terms of a correlated pairing state outside the N=28 closed shells with no pairing vibrations. Data were also obtained for 74Ge and 78Se

Villari, A.C.C.

HAL-CEA

Pair correlations in nuclei involved in neutrinoless double $\beta$ decay: $^{76}$Ge and $^{76}$Se

HAL-IN2P3

Precision measurements were carried out to test the similarities between the ground states of Ge76 and Se76. The extent to which these two nuclei can be characterized as consisting of correlated pairs of neutrons in a BCS-like ground state was studied. The pair removal (p,t) reaction was measured at the far forward angle of 3°. The relative cross sections are consistent (at the 5% level) with the description of these nuclei in terms of a correlated pairing state outside the N=28 closed shells with no pairing vibrations. Data were also obtained for Ge74 and Se78. © 2007 The American Physical Society

Villari, A. C C

The University of Manchester - Institutional Repository

Pair correlations in nuclei involved in neutrinoless double β decay: Ge76 and Se76

Villari, A. C.C.

LSU Scholarly Repository (Louisiana State Univ.)

Louisiana State University LSU Scholarly Repository Faculty Publications Department of Physics & Astronomy 5-3-2007 Pair correlations in nuclei involved in neutrinoless double β decay: Ge76 and Se76 S. J. Freeman The University of Manchester J. P. Schiffer Argonne National Laboratory A. C.C. Villari IN2P3 Institut National de Physique Nucleaire et de Physique des Particules J. A. Clark Yale University C. Deibel Yale University See next page for additional authors Follow this and additional works at: https://repository.lsu.edu/physics_astronomy_pubs Recommended Citation Freeman, S., Schiffer, J., Villari, A., Clark, J., Deibel, C., Gros, S., Heinz, A., Hirata, D., Jiang, C., Kay, B., Parikh, A., Parker, P., Qian, J., Rehm, K., Tang, X., Werner, V., & Wrede, C. (2007). Pair correlations in nuclei involved in neutrinoless double β decay: Ge76 and Se76. Physical Review C - Nuclear Physics, 75 (5) https://doi.org/10.1103/PhysRevC.75.051301 This Article is brought to you for free and open access by the Department of Physics & Astronomy at LSU Scholarly Repository. It has been accepted for inclusion in Faculty Publications by an authorized administrator of LSU Scholarly Repository. For more information, please contact ir@lsu.edu. Authors S. J. Freeman, J. P. Schiffer, A. C.C. Villari, J. A. Clark, C. Deibel, S. Gros, A. Heinz, D. Hirata, C. L. Jiang, B. P. Kay, A. Parikh, P. D. Parker, J. Qian, K. E. Rehm, X. D. Tang, V. Werner, and C. Wrede This article is available at LSU Scholarly Repository: https://repository.lsu.edu/physics_astronomy_pubs/1340 Pair Correlations in Nuclei Involved in Neutrinoless Double BetaDecay: 76Ge and 76Se.S.J. Freeman,1 J.P. Schiffer,2, ∗ A.C.C. Villari,3 J.A. Clark,4 C. Deibel,4S. Gros,2 A. Heinz,4 D. Hirata,3, 5 C.L. Jiang,2 B.P. Kay,1 A. Parikh,4P.D. Parker,4 J. Qian,4 K.E. Rehm,2 X.D. Tang,2 V. Werner,4 and C. Wrede41Schuster Laboratory, the University of Manchester, Manchester M13 9PL, UK2Argonne National Laboratory, Argonne, Illinois 60439, USA3GANIL (IN2P3/CNRS - DSM/CEA),B.P. 55027 14076 Caen Cedex 5, France4A.W. Wright Nuclear Structure Laboratory,Yale University, New Haven, CT 06520, USA5The Open University, Dept. of Physics and Astronomy, Milton Keynes, MK7 6AA, UK(Dated: September 17, 2021)AbstractPrecision measurements were carried out to test the similarities between the ground states of 76Geand 76Se. The extent to which these two nuclei can be characterized as consisting of correlatedpairs of neutrons in a BCS-like ground state was studied. The pair removal (p,t) reaction wasmeasured at the far forward angle of 3◦. The relative cross sections are consistent (at the 5% level)with the description of these nuclei in terms of a correlated pairing state outside the N=28 closedshells with no pairing vibrations. Data were also obtained for 74Ge and 78Se.PACS numbers: 25.40.-Hs, 27.50.+e, 23.40.-Hc∗Electronic address: schiffer@anl.gov1arXiv:nucl-ex/0701003v2  23 Mar 2007I. INTRODUCTIONInterest in the possibility of observing neutrinoless double beta decay (0ν2β) is consid-erable. If this decay were to be definitively observed, it would show that the neutrinos aretheir own antiparticles. In addition, the rate of the decay would be a measure of the neutrinorest mass, if the nuclear matrix element were known. Unfortunately, theoretical calculationsof this do not agree well with each other [1]. It seems appropriate to determine additionalproperties of the ground states of the possible 0ν2β systems by experiment, and thus helpconstrain and test theoretical calculations of this exotic decay mode. One of the likely candi-date nuclei is 76Ge decaying to the ground state of 76Se. We have started with a study of theproperties of the ground states of these nuclei, and especially the similarities and differencesbetween them, using transfer reactions. One part of this study is an accurate measurementof one-nucleon transfer in order to probe the occupation numbers of valence orbits for bothneutrons and protons, with particular attention to changes in these occupations. The otherpart is to study pair-correlations in these nuclei by nucleon pair transfer. Here we reporton a comparison of neutron pair transfer from the (p,t) reaction. We hope to obtain similardata on proton pair correlations from (3He,n) reactions in a future experiment.Pair transfer between 0+ states in the (p,t) or (t,p) reaction proceeds via L=0 transferand the angular distribution, for energies above the Coulomb barrier, is sharply forwardpeaked. This feature was recognized early [2] and was crucial in exploring the importanceof such correlations and their excitations, the so-called pairing vibrations [3]. The latterare an indication of deviations from the simplest pairing picture and can occur in regions ofchanging shapes, or when there is a gap in single-particle states, such as near a shell closure.We have carried out measurements of the neutron pair-removal (p,t) reaction on targetsof 74,76Ge and 76,78Se. The reaction on 78Se was measured because the 78Se(p,t)76Se leadsto 76Se, while 76Se(p,t)74Se starts from the ground state of 76Se. Thus both reactions arerelevant to the pairing structure of this ground state. The 74Ge target was included as acheck.There are two relevant aspects to these measurements. The first is the matter of pairingvibrations. The even Ge and Se isotopes are well studied and evidence for excited 0+states has been established [4, 5, 6] . In some of the lighter isotopes of Ge and Se, two-neutron transfer reactions have shown significant strength populating excited 0+ states.2These pairing vibrations indicate that there are significant BCS-like pair correlations inconnecting the target ground state in an even initial nucleus to excited 0+ states in thefinal. If there were significant differences in this regard between reactions leading to or from76Ge and 76Se, this would be an indication that the pair correlations in the initial and finalstates in double-beta decay differ. Any reliable calculations of the process would presumablyhave to reproduce such differences in order to obtain a reasonable matrix element for the0ν2β decay. Secondly, if accurate cross sections were available for pair transfer further checkscould be made of the similarity between the initial and final wave functions used in suchcalculations.II. EXPERIMENTAL CONSIDERATIONSGiven that the L=0 (p,t) transitions are the strongest in the spectrum of final statesat very forward angles, which is also the region where the approximations inherent in thedistorted wave Born approximation (DWBA) are best satisfied, it is desirable to carry outthese measurements as close to 0◦ as feasible. The (p,t) reaction had been studied previouslyon Ge [4] and Se [6] isotopes; relevant (t,p) measurements have also been made [7, 8, 9].Both the experimental methodology and the data analysis methods in the two (p,t) studieswere different (the target thickness was estimated from high-energy elastic scattering whereoptical model predictions are ambiguous, the angular distributions start at 7.5 degrees,and only angle-integrated cross sections are quoted, etc.), making a reliable systematiccomparison of Ge and Se data difficult. Our purpose here was to measure the cross sectionsat as far forward angles as feasible and to obtain a consistent set of accurate cross sectionswith particular care taken to reduce relative systematic uncertainties.The choice of energy was governed by the desirability of having both protons and tritonswell above the Coulomb barrier. For the present measurement we therefore chose 23-MeVprotons from the Yale ESTU tandem Van de Graaf accelerator. This energy is similar tothat used in earlier experiments, both for (p,t) and (t,p) reactions. Because one of theobjectives of the present measurement was to obtain accurate cross sections, we chose tomeasure the thickness of the evaporated germanium and selenium targets in situ by simplylowering the proton beam energy to 6 MeV, where the elastic scattering cross sectionsare very close to Rutherford values. The angle should not be so far forward that small3uncertainties in angle would become significant and 30◦ was chosen because calculationswith several optical potentials showed that the deviation from Rutherford scattering was lessthan 2%. The 76,74Ge and 78,76Se target thicknesses were found to range between 160 and400 µg/cm2. Since Se can sublimate at a relatively low temperature, this low-energy targetthickness measurement was made at the beginning and then at the end of the experiment;no significant differences (<3%) were observed. The highest beam currents used were about35 nA, though considerably lower (2-3 nA) for the 3◦ measurements.The Yale Enge split-pole spectrograph was used for the measurements with a focal-planedetector that cleanly separates tritons from other reaction products. As monitors, two Sisurface barrier detectors at ±32◦ were used. They were calibrated in terms of beam intensityusing a current integrator connected to a Faraday cup. The beam integrator was set to thesame scale that was used for the low-energy measurements and the solid-angle setting for theaperture of the spectrograph was also the same, thus establishing a relationship between anabsolute cross section scale in terms of the monitor yields, instead of the beam intergrator,for each target.The 3◦ setting for the spectrograph required that the Faraday cup be retracted so thatthe beam-current measurement had to rely on the previously calibrated monitor counters.Removal of the Faraday cup meant that the beam entered the spectrometer. The magneticrigidity of the tritons from the reaction is such that, with the magnetic field set for observingtritons, protons from the target cannot directly reach the focal plane and are interceptedinside the spectrometer. Protons scattered at this point can enter the focal plane and, whilstthey can be distinguished from tritons by their ionization density, they do impose a countingrate limit. As a result, the furthest forward angle where measurements could be made was3◦. Distorted-wave calculations indicate that the cross section at this angle is lower thanthat at 0◦ by about 8%. Spectra were also measured at the laboratory angle of 22◦ , whichis close to the minimum for L=0 angular distributions, though the location and depth ofthe minimum is very sensitive to the Q-value and the distorting parameters as is seen inFigure 1. Nevertheless, the ratio of the 3◦ to the 22◦ cross sections is huge compared to thatfor the other L values, and is therefore an excellent identifier of L=0 transitions, though theprecise value of this ratio will depend on the exact location and depth of the sharp minimumin the angular distribution.Representative spectra from the 3◦ measurements are shown in Figure 2 where the4ground-state transitions are clearly seen to dominate. The results of the cross-section mea-surements are shown in Table I below, with ratios to the ground-state cross sections givenonly for states with yields, at 3◦, larger than 1% of the ground state yield. The transitionswhere the ratio of cross sections between 3◦ and 22◦ is consistent with L=0 are shown inbold. More complete data, though at further back angles and with less attention to accuraterelative cross sections had been reported, but the emphasis in these previous measurementswas on angular distributions starting at 7.5◦, and only angle-integrated cross sections arequoted [4, 5]. The uncertainty in the present experimental cross sections is believed to be±10%, while that in the relative values is estimated at ±5 %. These uncertainties are dom-inated by estimates of systematic errors (constancy of the beam spot on target, accuracyof angle determinations in the monitors, possible small drifts in monitor calibration, pos-sible inefficiency in the focal plane detector, uniformity of target thickness etc.) while thestatistical contribution is of the order of 1%.The (p,t) differential cross sections at 3◦ for populating the 0+ ground states for the fourtargets are very similar: 6.4, 6.7, 6.0, and 7.1 mb/sr for 74,76Ge and 76,78Se respectively.Excited 0+ states stand out in the ratio between the 3◦ and 22◦ yields, which is an order ofmagnitude larger than for any other excited state. With the exception of the 74Ge target,none of these excited 0+ states is populated with a cross section at 3◦ that is more than 2%of that leading to the ground states. In the 74Ge(p,t)72Ge reaction the cross section to thefirst-excited 0+ state is 1.9 mb/sr. This feature is well known [4] as an example of a pairingvibration. The case of 74Ge is illustrative of effects that can be problematic; however thecontext of the current work is related only to the 76Ge/76Se double-beta-decay system.III. DWBA CALCULATIONSThe calculations were carried out with the DWBA program PTOLEMY [10] to correctthe dependence of the reaction on Q-values. The consideration of the details of nuclearstructure is beyond the scope of this study, even though 76Ge and 78Se have 6 neutronvacancies in the N=50 shell, 74Ge and 76Se have 8. The form factor for the neutron pair wascalculated assuming a mass-2, ` = 0 di-neutron bound in a Woods-Saxon potential with theappropriate binding energy and having 3 nodes in its wave function. The proton potentialswere those of Ref. [11] and the triton potential that of Ref. [12]. The measured cross sections5at 3 degrees are given in Table II together with the ratio of the experimental cross sections tothe calculated values. The absolute magnitude of the DWBA cross section is very sensitiveto the choice of the distorting potentials as is the location of the first minimum in the angulardistribution. However, all calculations indicate that the relative values between these targetsof the calculated cross sections at 3◦ remain the same (within 10%) with various reasonablepotentials for protons and tritons.With the proton potential of Ref. [11], the average ratio changes from 136 to 217. Theexperimental cross sections by themselves are remarkably constant; without any correctionfor reaction dynamics they vary by ±6%. Dividing the experimental numbers by the cal-culated reaction cross sections, reduced the difference between 76Ge and 76Se even further.However, this improvement is probably not significant, in view of the estimated 5% relativeerror and the neglect of the different numbers of neutrons. The peak cross sections andDWBA trends are also shown in Figure 3.IV. PAIR-ADDING REACTIONSThe pair-adding (t,p) reaction had been studied previously, for both the 74Ge(t,p)76Ge[7, 8] and the 76Se(t,p)78Se [9] reactions. While the ground-state transitions are the same asthe ones studied here, transitions to excited states could, in principle, show up and indicatepairing vibrations. While the angular distributions were not measured at as far forwardangles as in the present work, some estimate can be obtained by comparing integral crosssections. No excited 0+ states were seen in these (t,p) studies with a strength greater than4% of the ground-state transition, confirming the dominance of pair correlations in theground states of these nuclei, with no splitting into pairing vibrations.V. CONCLUSIONSThe experimental cross sections measured in this experiment are remarkably constant forground-state transitions with the various targets. The difference between 76Ge and 76Se, inthe ratio of the experimental ground-state transition strengths divided by the appropriateDWBA calculations, is less than the 5% estimated accuracy of the measurements. Tran-sitions to excited 0+ states from 76Ge and 76Se targets are no more than a few percent of6the ground-state transitions indicating no sign of the pairing vibrations that appear in someof the lighter isotopes. Had such admixtures been present, this would have complicated asimple comparison of the ground states. The constancy of the ground-state strength in paircorrelations seems to be as true for neutron-pair-adding transfers leading to these nuclei asit is for pair removal from them. The present results suggest that the ground states of 76Geand 76Se exhibit quantitatively very similar neutron pair-correlations. Changes in pairingare thus unlikely to be a significant complicating factor in the wave functions of these statesfor calculations of neutrinoless double β decay.We wish to acknowledge helpful discussions with S.C. Pieper, Ben Bayman, and M.H.Macfarlane. The help of John Greene in meticulous work on target preparation is alsoacknowledged. The work was supported by the U.S. Department of Energy, Office of Nu-clear Physics, under contracts DE-FG02-91ER-40609 and DE-AC02-06CH11357, the UKEngineering and Physical Sciences Research Council, and IN2P3/CNRS-France.[1] J.N. Bahcall, H. Murayama, and C. Peña-Garay, Phys. Rev. D70, 033012 (2004).[2] S. Yoshida, Nucl. Phys. 33, 685 (1962).[3] D.R. Bes and R.A. Broglia, Nucl. Phys 80, 289 (1966).[4] D. Guilbault et al., Phys. Rev. C16, 1840 (1977).[5] D. Ardouin et al., Phys. Rev. C18, 1201 (1978).[6] M. Borsaru et al., Nucl. Phys. 284, 379 (1977).[7] S. Mordechai et al., Phys Rev. C18, 2498 (1978).[8] C. Lebrun et al., Phys. Rev. C19, 1224 (1979).[9] D.L. Watson and H.T. Fortune, Phys. Rev. C35, 430 (1987).[10] M.H. Macfarlane and Steven C. Pieper, ANL-76-11 Rev. 1 Argonne National LaboratoryReport (1978) unpublished.[11] F.D. Becchetti and G.W. Greenlees, Phys. Rev. 182, 1190 (1969).[12] R. Perry, Phys. Rev. C24, 1471 (1981).[13] F.G. Perey, Phys. Rev. 131, 745 (1963).7FIG. 1: (Color online) DWBA calculations of ground-state angular distributions at 23 MeV fordifferent targets, using the proton optical potentials of Ref. [12] and the triton potential fromRef. [7]. The intent of the figure is to illustrate the sensitivity of the shapes of the angulardistributions to the Q-values, while the peak cross sections remain relatively stable. The relativevariation in the peak cross sections for different choices of potentials is very similar.8FIG. 2: (Color online) Spectra of tritons at 3◦ measured with the Yale split-pole spectrograph,normalized to 100 for the ground-state peak, and labeled in each case by the target nuclide. Thepeaks corresponding to L=0 transitions are identified by a pointer. Peaks due to isotopic impuritiesare marked by an x. While there is evidence in 74Ge(p,t)72Ge of substantial strength in a low-lyingexcited 0+ state, there are no large admixtures seen for the 76Ge and 76Se targets.9FIG. 3: (Color online) The ground-state 0+ to 0+ cross sections at 3◦ are plotted as a functionof Q-value, for convenience in display. Also shown are the DWBA cross sections multiplied by oneaverage normalization factor for each proton potential. The estimated relative errors are shown onthe experimental points.10TABLE I: Summary of (p,t) cross sections at 3◦ and the ratio (in %) of these to the 22◦ values.Transitions consistent with L=0 are shown in boldface.74Ge(p,t)72Ge σgs(lab) = 6.4 mb/srExcitation Energy (keV) (σ/σgs)3◦ Ratio(3◦/22◦)0 100 86691 29 280834 2.8 0.91464 0.5 1.52024 0.5 42762 0.9 13076Ge(p,t)74Ge σgs(lab) = 6.7 mb/srExcitation Energy (keV) (σ/σgs)3◦ Ratio(3◦/22◦)0 100 50596 3.2 1.01204 1.1 1.61463 2.2 0.82198 2.9 32833 1.7 676Se(p,t)74Se σgs(lab) = 6.0 mb/srExcitation Energy (keV) (σ/σgs)3◦ Ratio(3◦/22◦)0 100 115635 1.0 0.4854 1.4 8078Se(p,t)76Se σgs(lab) = 7.1 mb/srExcitation Energy (keV) (σ/σgs)3◦ Ratio(3◦/22◦)0 100 150559 1.2 0.41121 0.8 41220 0.7 1.011TABLE II: 3◦ laboratory cross sections and ratios to DWBA. Cross sections are for the ground-state to ground-state transitions.Target σexp(lab) σDWBA σexp/σDWBA(mb/sr) (mb/sr)74Ge 6.4 0.0438 14776Ge 6.7 0.0499 13576Se 6.0 0.0437 13778Se 7.1 0.0431 16412

Pair correlations in nuclei involved in neutrinoless double beta decay:
  76Ge and 76Se

Pair correlations in nuclei involved in neutrinoless double beta decay: 76Ge and 76Se

Abstract

Similar works

Full text

Available Versions

HAL-CEA

HAL-IN2P3

The University of Manchester - Institutional Repository

LSU Scholarly Repository (Louisiana State Univ.)

The University of Manchester - Institutional Repository