A recent 20O(d,p)21O experiment, in reverse kinematics, discovered two new states in 21O at 4.77(10) and 6.17(11) MeV, with Jπ assignments of 3/2+ and of 3/2+ or 7/2−, respectively. Both widths and spectroscopic factors were reported, along with the branching ratio for the upper state to decay to the 2+ state of 20O. We have computed single-particle widths for all the relevant decays and have used them to extract additional information for these two states, including the spectroscopic factors for 2+ decay of the upper state with the two possible Jπ values. Our analysis prefers 7/2− for Jπ

Fortune, H Terry

Sherr, Rubby

English

ScholarlyCommons@Penn

University of PennsylvaniaScholarlyCommonsDepartment of Physics Papers Department of Physics2-14-2012Widths and Spectroscopic Factors in ²¹OH Terry FortuneUniversity of Pennsylvania, fortune@physics.upenn.eduRubby SherrPrinceton UniversityFollow this and additional works at: http://repository.upenn.edu/physics_papersPart of the Physics CommonsFortune, H. T. and Sherr, R. (2012). Widths and Spectroscopic Factors in 21O. Physical Review C, 85(2), 027305. doi: 10.1103/PhysRevC.85.027305.© 2012 American Physical SocietyThis paper is posted at ScholarlyCommons. http://repository.upenn.edu/physics_papers/227For more information, please contact repository@pobox.upenn.edu.Recommended CitationFortune, H. T., & Sherr, R. (2012). Widths and Spectroscopic Factors in ²¹O. Retrieved from http://repository.upenn.edu/physics_papers/227Widths and Spectroscopic Factors in ²¹OAbstractA recent 20O(d,p)21O experiment, in reverse kinematics, discovered two new states in 21O at 4.77(10) and6.17(11) MeV, with Jπ assignments of 3/2+ and of 3/2+ or 7/2−, respectively. Both widths and spectroscopicfactors were reported, along with the branching ratio for the upper state to decay to the 2+ state of 20O. Wehave computed single-particle widths for all the relevant decays and have used them to extract additionalinformation for these two states, including the spectroscopic factors for 2+ decay of the upper state with thetwo possible Jπ values. Our analysis prefers 7/2− for Jπ.DisciplinesPhysical Sciences and Mathematics | PhysicsCommentsFortune, H. T. and Sherr, R. (2012). Widths and Spectroscopic Factors in 21O. Physical Review C, 85(2),027305. doi: 10.1103/PhysRevC.85.027305.© 2012 American Physical SocietyThis journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/227PHYSICAL REVIEW C 85, 027305 (2012)Widths and spectroscopic factors in 21OH. T. FortuneDepartment of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USAR. SherrDepartment of Physics, Princeton University, Princeton, New Jersey 08544 USA(Received 8 August 2011; published 14 February 2012)A recent 20O(d,p) 21O experiment, in reverse kinematics, discovered two new states in 21O at 4.77(10) and6.17(11) MeV, with J π assignments of 3/2+ and of 3/2+ or 7/2−, respectively. Both widths and spectroscopicfactors were reported, along with the branching ratio for the upper state to decay to the 2+ state of 20O. We havecomputed single-particle widths for all the relevant decays and have used them to extract additional informationfor these two states, including the spectroscopic factors for 2+ decay of the upper state with the two possible J πvalues. Our analysis prefers 7/2− for J π .DOI: 10.1103/PhysRevC.85.027305 PACS number(s): 27.30.+t, 21.60.Cs, 21.10.Jx, 23.20.LvNeutron-rich nuclei have turned out to be a good laboratoryfor finding new magic numbers and eliminating others, andfor fine tuning the shell-model interaction to be used incalculations of nuclei far from stability. Excitation energies,Jπ values, and spectroscopic factors are important for structuremodels as they evolve to account for properties of suchnuclei. One recent example is an investigation [1] of the20O(d,p) 21O reaction, in reverse kinematics. They measuredangular distributions for four states, at excitation energies of0, 1.213(7), 4.77(10), and 6.17(11) MeV. For the ground state(g.s.), their results were consistent with an earlier assignment[2] of Jπ = 5/2+. They assigned Jπ = 1/2+ for the stateat 1.21 MeV, based on its  = 0 angular distribution. Theyidentify this state as the one previously reported at 1.33(9) [3]and 1.218(4) [4] MeV. They did not observe a probable 3/2+state reported [3,4] at 2.13 MeV.The unbound state at 4.77 MeV has a clear  = 2 angulardistribution. The authors assign Jπ = 3/2+ to this state, onthe grounds that its spectroscopic factor of 0.58(14) is toolarge for a 5/2+ excited state. The angular distribution for the6.17-MeV state is consistent with either  = 2 or 3, leading toa suggestion of Jπ = (3/2+ or 7/2−). From coincident gammarays connecting the 2+ and g.s. of 20O, they report a branchingratio (BR) for this state of 2+ /tot = 0.71(22). Quantitiesmeasured in Ref. [1] for these two unbound states are listed inTable I.In the present report, for the two unbound states, we exploitthe well-known relationship between width and spectroscopicfactor ( = Ssp, where sp is the single-particle (sp)width computed in a potential model) to determine whetheradditional information can be extracted for these states.Comparison of the spectroscopic factor computed from thewidth to the one obtained from a transfer reaction has longbeen [5] a powerful tool for determining  values. Our spwidths are also listed in Table I. They were calculated in aWoods-Saxon well, with r0 = 1.25 fm and a = 0.65 fm. Welook first at the 6.17-MeV state, which has S = 0.30(7) or0.20(5) for  = 2 or 3 respectively, and a BR to the 2+ stateof 2+/tot = 0.71(22). As there are only two open channels,the rest of the decay width is for the g.s. These spectroscopicfactors, together with sp widths from Table I, give g.s. widthsof 330(80) or 19(5) keV for  = 2 or 3 respectively—to becompared with the experimental width of 320(260) keV. Asthis width is only 1.2σ from zero, it might be thought thatit contains very little information. However, let us see whattranspires.Because the  = 3 sp width for decay to the 2+ state is only1.6 keV, if the state is 7/2− the decay to 2+ is almost certainlynot  = 3, but  = 1. The  = 1 sp width is 860 keV. We thenask, what value of  = 1 spectroscopic factor S1 for 7/2− →2+ is needed to fit the observed BR? And then, what does thisS1 imply about the total width? From Table I, the g.s. width,if 7/2−, is 19(5) keV. The 2+ width is 860S1 keV. We plotthe BR computed from these widths as a function of assumedS1 in Fig. 1. In our figures, we make use of the total width,the BR, and the spectroscopic factors from the (d,p) reaction,through the constraint g.s. = Ssp, at the ±1σ level. We noteagreement with the experimental BR for 0.02 < S1 < 0.29. Wethen plot the total width versus assumed S1 in Fig. 2. (Note thesemilogarithmic scale.) Again, we have agreement, this timefor 0.05 < S1 < 0.65. Thus, if the 6.17-MeV state is 7/2−,then an  = 1 spectroscopic factor of 0.05 < S1 < 0.29 forp-wave decay to the 2+ state fits both the BR and the totalwidth. Reference [1] also mentioned that decay of a 7/2− stateto the 2+ could be by p3/2.For the 3/2+ possibility, decay to the 2+ state could be via = 0 or 2. Unbound states with  = 0 are odd entities, and an= 0 partial decay branch might be expected to distort the peakshape. As no such distortion is apparent, we will first assumethe decay to 2+ is via  = 2. But, this assumption remains tobe tested. We return to this point below. For 3/2+, from thereported spectroscopic factor, the g.s. width is 330(80) keV.The 2+ width is 62S2 keV. Again, we plot the computed BRversus assumed S2 in Fig. 3. First, we briefly discuss theallowed range of S2. In the simplest shell-model calculation,for any state in 21O the sum of S’s to all positive-parity states of20O is 5. This includes  = 0 and 2. For any 0+ state in 20O, Smust be less than 1, but that limit does not hold if J (20O) = 0.027305-10556-2813/2012/85(2)/027305(4) ©2012 American Physical SocietyBRIEF REPORTS PHYSICAL REVIEW C 85, 027305 (2012)TABLE I. Quantitative information for two unbound levels in 21O. (Energies and widths in MeV.)Ref. [1] PresentEx En   Jπ S sp g.s. = Ssp b4.77(10) 0.96(10) 0.46(20) 2 3/2+ 0.58(14) 0.145 0.084(20)6.17(11) 2.36(11) 0.32(26) 2 3/2+ 0.30(7) 1.10 0.33(8)3 7/2− 0.20(5) 0.096 0.019(5)0.68a 1 0.86a2 0.062a3 1.6 × 10−3aaFor decay to the 2+ state.bUsing S from column 6 and our sp widths.Even if the 3/2+ state has a large amount of d3/2 sp strength,the value of S to the 2+ state will also contain d5/2 strength. Itis unlikely, however, that S to the 2+ state is as large as, say, 3.From Fig. 3, we note that, in order to fit the BR at the 1σ level,we must have S2 > 3.4, above the limit of reasonableness.The curve labeled f is for  = 3 decay to the 2+ state. It isclear, as alluded to above, that no amount of  = 3 will fit theBR. The total width (Fig. 4, again semilogarithmic) provideslittle additional information because any value of S2 producesagreement (but see Fig. 5). Again, there is no agreement for = 3.For the 6.17-MeV state, we conclude that the data of Ref. [1]are internally consistent for a Jπ value of 7/2− if the decayto the 2+ state is p wave with S1 in the range 0.05–0.29. ForJπ = 3/2+, and d-wave decay to the 2+ state, the data wouldrequire S2 > 3.4 to be consistent at the 1σ level. This mayindicate that most of the 2+ decay is s wave. Independentlyof the  = 0,2 admixture for decay to 2+, if the state is 3/2+,21O(6.17) pf00.510 0.05 0.1 0.15 0.2S(2+)BRFIG. 1. (Color online) Branching ratio 2+/tot for 21O(6.17).Squares represent the experimental value, with dashed horizontallines at the ±1σ limits. Plotted vs the assumed S1, the solid curveis the BR for J π = 7/2−, assuming  = 1 for decay to 2+. Theshort-dashed curves are at ±1σ .in order to have agreement with the BR at the 1σ level, thewidth to the 2+ state (see Fig. 5) must be >240 keV, whilefor agreement with the measured total width at the 1σ levelthis width must be <330 keV. So, for the 3/2+ possibility wehave (at the 1σ level) 240 keV < 2+ < 330 keV. If this isall (or mostly) s-wave decay, we leave for others the task ofconverting this width into an  = 0 spectroscopic factor. In allof the above, we have used the expression  = Ssp to convertmeasured S’s into g.s. widths.A value of 285(45) keV for decay to the 2+ state wouldleave 35(265) keV for the g,s, width, to be compared withthe g.s. width of 330(80) keV computed from the reportedspectroscopic factor. Alternatively, the sum of g.s. (from S)and 2+ (from BR) is 615(92) keV, compared to the reportedtotal width of 320(260) keV. Inspection of the spectrum wouldappear to rule out a possible total width of 615(92) keV.Consideration of all this information (including the absenceof any obvious peak distortion) leads us to conclude that 7/2−is more likely than 3/2+ for the upper state.21O(6.17) pf1010010000 0.05 0.1 0.15 0.2S(2+)tot (keV)FIG. 2. (Color online) Total width of the 6.17-MeV state of 21O.Squares with horizontal dashed lines are the experimental result. Thesolid curve is for 7/2−, plotted vs the assumed value of S1.027305-2BRIEF REPORTS PHYSICAL REVIEW C 85, 027305 (2012)21O(6.17)00.20.40.60.810 1 2 3 4 5 6S(2+)BRexpdfFIG. 3. (Color online) Experimental BR as in Fig. 1. Solid curves,with dashed curves at ±1σ , are computed BRs, assuming bothbranches have the same  value (d or f ).We turn now to the 4.77-MeV state, whose width is0.46(20) MeV. With a spectroscopic factor of 0.58(14), thewidth should have been 84(20) keV—quite a large differencefrom the stated width. In their data the total width of the4.77-MeV peak appears to be about 1.44 MeV. The authors donot state the resolution width at this energy, but they do give thefull width at half maximum (FWHM) at the 1.21-MeV state as0.77(17) MeV. They state that they extracted the natural widthby convoluting Gaussian and Breit-Wigner shapes. With theirquoted width of 0.46(20) MeV and our estimate of a total widthof 1.44 MeV in their spectrum, we deduce a FWHM of about0.85 MeV for the resolution at 4.77 MeV. This is reasonablyclose to the value of 0.77(17) they quote for 1.21 MeV. Thewidth measured directly by Ref. [1] from their spectrum differsfrom the width calculated from the spectroscopic factor by an21O(6.17)1010010000 1 2 3 4 5 6S(2+) tot (keV)expdfFIG. 4. (Color online) As in Fig. 3, but for total width. (Notesemilogarithmic scale.)21O(6.17)00.510 50 100 150 200 250 300Width to 2+ (keV)BR7/2-3/2+FIG. 5. (Color online) As in Fig. 1, but for both 7/2− and 3/2+,plotted vs assumed width for decay to 2+.amount 0.38(19) MeV—about a 2σ difference. Another wayto state this discrepancy is to compute S from the measuredwidth and compare it to the S extracted from comparison ofmeasured cross section to a distorted-wave calculation. UsingS = exp/sp and our sp of 145 keV, we get S = 3.2(1.4).Of course, this S must rigorously be less than unity. The valueof S from the cross section is Sσ = 0.58(14). The ratio of thetwo (which should be 1.0) is 5.5(20). As this is not a 3σ effect,it is not clear how seriously to take this discrepancy. Perhapsanother look at this reaction might be worthwhile.To summarize: If the 6.17-MeV state is 7/2−, the 2+ decayis almost certainly via  = 1, with S1 in the range 0.05–0.29.If it is 3/2+ and the 2+ decay is d wave, the BR requires S2 >3.4—which is very unlikely. These results are summarized inTable II. If the 6.17-MeV state is 3/2+, decaying to the 2+state by a combination of  = 0 + 2, the partial 2+ width isexc = 285(45) keV. The g.s. width is 330(80), obtained fromthe reported [1] spectroscopic factor and our sp width (Table I).As these are the only open channels, the total width is then615(92) keV, to be compared with the measured width [1] of320(260) keV.TABLE II. Partial and total widths (keV) for the 6.17-MeV statefor various J π and  combinations.J π  to 2+ exca g.s.b totc measd3/2+ 2 Not possible0 + 2 285(45) 330(80) 615(92) 320(260)7/2− 3 Not possible1 146(103) 19(5) 165(103) 320(260)aWidth for decay to 2+ obtained from reported BR [1] and presentanalysis.bFrom Table I.ctot = exc + g.s..dTotal width reported in Ref. [1].027305-3BRIEF REPORTS PHYSICAL REVIEW C 85, 027305 (2012)If the state is 7/2−, the data do not allow  = 3 for the2+ decay, but  = 1 is acceptable, giving an excited-statewidth of exc = 146(103) keV. The g.s. width obtained fromthe reported S is 19(5) keV, resulting in a total width of165(103) keV, to be compared with the measured width of320(260) keV. Thus, our results favor Jπ = 7/2− for this state,even though the 3/2+ possibility is allowed at the 1.1σ level.For the two Jπ possibilities, the total widths that result fromour analysis differ by 3.2σ . So, even a modest reduction inthe uncertainty of the experimental width should allow a clearchoice.For the 4.77-MeV state, the spectroscopic factor derivedfrom the measured width is 5.5(20) times the S derived fromthe measured (d,p) cross section.[1] B. Fernandez-Dominguez, J. S. Thomas, W. N. Catford,F. Delaunay, S. M. Brown, N. A. Orr, M. Rejmund, M. Labiche,M. Chartier, N. L. Achouri, H. Al Falou, N. I. Ashwood,D. Beaumel, Y. Blumenfeld, B. A. Brown, R. Chapman,N. Curtis, C. Force, G. de France, S. Franchoo, J. Guillot,P. Haigh, F. Hammache, V. Lapoux, R. C. Lemmon, F. Mare´chal,A. M. Moro, X. Mougeot, B. Mouginot, L. Nalpas, A. Navin,N. Patterson, B. Pietras, E. C. Pollacco, A. Leprince, A. Ramus,J. A. Scarpaci, N. de Se´re´ville, I. Stephan, O. Sorlin, and G. L.Wilson, Phys. Rev. C 84, 011301(R) (2011).[2] E. Sauvan, F. Carstoiu, N. A. Orr, J. C. Ange´lique, W. N. Catford,N. M. Clarke, M. Mac Cormick, N. Curtis, M. Freer, S. Gre´vy,C. Le Brun, M. Lewitowicz, E. Lie´gard, F. M. Marque´s,P. Roussel-Chomaz, M. G. Saint Laurent, M. Shawcross, andJ. S. Winfield, Phys. Lett. B 491, 1 (2000); E. Sauvan,F. Carstoiu, N. A. Orr, J. S. Winfield, M. Freer, J. C. Ange´lique,W. N. Catford, N. M. Clarke, N. Curtis, S. Gre´vy, C. Le Brun,M. Lewitowicz, E. Lie´gard, F. M. Marque´s, M. Mac Cormick,P. Roussel-Chomaz, M. G. Saint Laurent, and M. Shawcross,Phys. Rev. C 69, 044603 (2004).[3] W. N. Catford, L. K. Fifield, N. A. Orr, and C. L. Woods, Nucl.Phys. A 503, 263 (1989).[4] M. Stanoiu, F. Azaiez, Zs. Dombra´di, O. Sorlin, B. A. Brown,M. Belleguic, D. Sohler, M. G. Saint Laurent, M. J. Lopez-Jimenez, Y. E. 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Widths and Spectroscopic Factors in ²¹O

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Widths and Spectroscopic Factors in ²¹O

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