m' ABSORPTION AND THE DISTRIBUTION OF NEUTRONS. . .

proton radii equal- is shown in Fig. 3; it is asmuch as 8.8% for Pb.

IV. CONCLUSIONS AND COMMENTS

The ratio of w'/w absorption cross sections issensitive to details of the neutron density, assum-ing the proton density is known already, e.g.,from electron scattering. It provides a useful con-straint on the neutron distribution —one which con-tains information about the nuclear surface, al-though it does not fix uniquely a particular momentor parameter. An accuracy of a fem tenths of apercent in the ratio is required for interesting re-sults. The validity of the optical model used can

be verified by studying the energy dependence ofthe cross sections' and of the ratios, ' and is itselfan interesting question worth further study. Notethat the ratios are quite insensitive to the opticalparameters used. '

Differential elastic w scattering data will alsobe quite sensitive to details of the nucleon densi-ties, particularly at large momentum transfers. 'This will be explored in a later paper.

ACKNOWLEDGMENT

One of us (MMS) would like to thank Los AlamosScientific Laboratory for its hospitality. J. Silverand A. Lopez assisted with the computations.

*Research supported in part by the National ScienceFoundation. Part of this woxk was done while the authorwas a Visiting Staff Membex at Los Alamos ScientificLaboratory.

&Work perfox'med under the auspices of the U. S. Atom-ic Enexgy Commission.

«E. H. Auerbach, H. M. Qureshi, and M. M. Sternheim,Phys. Rev. Letters 21, 162 (1968).

2A. Abashian, R. Cool, and J. W. Cronin, Phys. Rev.104, 855 (1956),

36. W. Greenlees, G. J. Pyle, and Y. C. Tang, Phys.Rev. Lettexs 17, 33 {1966); Phys. Rev. 171, 1115 {1968).

46. W. Greenlees, W. Makofske, and G. J. Pyle, Phys.Rev. C 1, 1145 (1970).

50. Slanina and H. McManus, Nucl. Phys. A116, 271(1968).

"E.H. Auerbach and M. M. Sternheim, BrookhavenNational Laboratory Report No. BNL-12696, 1968 {un-published) .

VL. S. Kisslinger, Phys. Rev. 98, 761 (1955}.SE. H. Auerbach, D. M. Fleming, and M. M. Sternheim,

Phys. Rev. 162, 1683 (1967); 171, 1781 (1968).9F. Binon et a/. , Rucl. Phys. 817, 168 (1970).

«OM. M. Sternheim and E. H. Auerbach, Phys. Rev. Let-ters 25, 1500 (1970).

««M. Crozon eta/. , Nucl. Phys. 64, 567 {1965).«2The units for 5 used in the table and in the ABACUS-M

code are F . Thus in Eq. (3}o'is expressed in F and Pin F

«3A. Donnachie, R. G. Kirsopp, and C. Lovelace, Phys.Letters 268, 161 (1968); see also CERN Report No. TH-838, addendum (to be published).

PHYSICAL REVIEW C VOLUME 4, NUMBER 5 NOVEMBER 1971

High-Spin Proton States Observed in the Reactions Zr(n, r) Nb and Mo(n, r) Tc

at 50 MeV

M. 8. Zisman and B.G. HarveyI.ambience Belle/ey Laboratory, University of Ca/ifoxAia, Berke/ey, Ca/ifornia 94720

(Received 16 April 1971)

The reactions ~ Zr(&, t )9 Nb and 92Mo(0. , t)93Tc have been investigated with a 50-MeV O. -par-ticle beam from the Berkeley 88-in. cyclotron. Comparisons are made with the results of( He, d ) experiments on the same targets in ordex to locate high-spin (l & 2) levels in 9«Nb and93Tc. The ~«Nb(4. 18 MeV) and 3Tc(3.91 MeV) levels are probable l =4 or 5 levels, in contrast tothe (3He, d ) results. A difference in Q values for the reactions 90Zr(0,', t)9«Nb and 9«Zr(0', t)-92Nb of 680+ 25 keV yields a Q value for the reaction 90Zr(e t)9«Nb of -14.643+ 0.027 MeV,which is not consistent with the presently accepted mass excess of -86.750+ 0.06 MeV for"Nb.

I. INTRODUCTION

In recent years there have been many studies' 'of proton configurations in the N = 50 nuclei

O'Nb and O'Tc. The locations of these proton statesare of interest for comparison with shell-modelcalculations~' and the centroid positions are use-ful in predicting energies of two-particle proton-

B. G. HARVEY

neutron states in nearby odd-odd nuclei. Thestates expected in proton transfer to ' Zr and "Moare (suppressing radial quantum numbers) ga/»g //g ds /2 d3 /2 s$ /2 and possibly h»» . The ('He, d)reaction, homever, preferentially populates thelower-angular-momentum states (i.e., I=0, 2).Thus, it is not a very efficient method for locatinghigh-spin states such as g„„g,~„or A»„, par-ticularly if these states are fragmented into manylevels. In the "Mo('He, d)~'Tc reaction, which hasbeen studied in detail at 18 and 35 MeV, ' ' no / =4levels have been reported except for the groundstate, although several have been seen in the "Zr-('He, d)"Nb experiments. "~'8 The large momen-tum transfer in the (a, f) reaction, compared withthat in the ('He, d} reaction, favors the excitationof high-angular-momentum proton states. [Q xR~ 6 for the (a, t) reaction at 50 MeV on "Zr.] Acomparison of the relative strengths of variousstates observed in both the ('He, d) and (o., t) re-actions should, therefore, give some informationon the location of high-orbital-angular-momentum(I= 4 or 5) levels in "Nb and "Tc.

II. EXPERIMENTAL

The experiment was performed with a 50-MeVe-particle beam from the Berkeley 88-in. cyclo-tron at a beam resolution, hE/E, of 0.04%. Thetargets mere self-supporting metal foils of '~Zr(enriched to 9V.8%}and "Mo (enriched to 98.3%),whose nominal thicknesses were 0.20 and 0.30 mg/em', respectively. Due to large uncertainties inthe target thicknesses, absolute cross sectionsfor both reactions are accurate only to about +50/p.Relative cross sections for each target, however,should be correct to +15%. Tritons were detectedwith tmo counter telescopes, each consisting of a0.25-mm phosphorus-diffused Si ~E and 5-mmSi(Li) E detector, and identified with a Goulding-Landis particle identifier. '

HI. RESULTS AND DISCUSSION

A. Zr(n, t) Nb

Since the previously reported level energiesfrom "Zr('He, d}"Nb experiments"" indicaterather substantial discrepancies, me remeasuredthem. [The energies reported in Refs. 1 and 6 aresystematically higher than those found in Ref. 2,and the differences appear to increase with excita-tion energy. I"or example, the strongest peak in

Zr( He~ d} Nb ls assigned excitation energies of3.360 +0.015,' 3.395 ~ 0.015,' and 3.410 ~ 0.010'MeV.] Our spectra were calibrated with the '~F(g.s.)impurity peak and "Nb(g. s.) peak as a function ofangle. " The Q value for the "O(n, t)"F reaction,-19.2136 MeV, mas taken from published tables. "However, recent results of various reactions lead-ing to "Nb give conflicting results for the massexcess of that nucleus.

A "Zr('He, d)"Nb experiment' gives a Q valueof -0.22V+0.020 MeV, which is essentially identi-cal to the published" Q value obtained from theMass Table of Mattauch, Thiele, and Wapstra. "But the "Zr(p, n)"Nb reaction" gives Q =-2.045+0.006 MeV, mhich changes the mass excess of"Nb used in Ref. 11 by +120 keV. Our mass of O'Nb

comes from the relative Q values of the Zr(a, t)-"Nb and "Zr(n, t)~2Nb reactions, which were ob-served'4 simultaneously with a O'Zr target con-taining about 5% 'OZr impurity. The energy cali-bration of the "Zr(o., t) dat:a [using the "F(g.s.)and "Nb(g. s.}as a function of angle, with Q valuesas given in Ref. 11] gives a difference in Q valuesof 680 + 25 keV between the 90Zr(o. , t)"Nb and "Zr-(c., t) 'Nb reactions. Ball and Cates" found a dif-ference in ('He, d} Q values for the two isotopes of6VV ~ V keV, mhieh is essentially identical to our(c., t) results" and has a much lower uncertainty.The difference in Q values obtained by Ball andCates" corresponds to a "Zr('He, d)"Nb Q value

TABLE I. Summary of Q values for reactions relating to 9~Nb.

HeactionMeasured Q value

(MeV)

Published Q value ~

{MeV)

9~Nb mass excess"(MeV}

"zr('He, d)"NbI~zr(e, t)92Nb

Zr(P w ) Nb"Zr('He, d)"Nb '

II

'Ozr(0. , t)"Nb

—2.045+0.006-0.227+0.020-0.319~0.013'

—14,643 +0,027

0.358 +0.011-13.963+0.011-1.925 +0.060-0.225+ 0.060

II

-14.545 +0.060

-86.630+0.008-86.748+0.020-86.656 +0.014-86.652 +0.027

Taken from gef. 11, which uses a mass excess for Nb (from Ref. 12) of -86.750 +0.060 MeV.b Calculated from the difference between the measured and puMished Q values.c Reference 13.d Reference 6.c Relative to ~~Zr(38e, d)92Nb Q value listed above. Q-value difference from Ref. 15 (see text).

Relative to O'Zr(n, t)9 Nb Q value listed above. Q-value difference from Hef. 14 {see text).

HIGH - SPIN PROTON STATES OBSERVED IN. ..

TABLE II. Levels observed in the reaction SOZr(e, t)9~Nb at 50 MeV.

No. ,Levels

observed ~

(MeV)Intensity b

(mb)

Levelsobservedc, d

(MeV)

/He, d)

C29 d

S~Mo(g.s.) decayLevels

observed c

(MeV)

0.0(o.1o3) '1.29

3,4410.144O.O38 ~

0.073

O.O69 ~

0.00.1031.31

0.9180.430o.o4s"

O.O78"

o.o58"

1,5811.6371,791

1.95 +0.042.302.39+0.032.532,61

2.772.903.01

3.12+0.04

3.65+0.04

%'eakO.O43 ~

%'eakO.O32'0.023 ~

O.O12 ~

0.0740 036m

%'eak

0.218

0.027 ~

3.073.11

3 9211

O.O14"0.017"

%'eak ~

0.035

0.388

O.O23"

%eak ~

(2.391)&

2.5312.631

2.792

3.028

3,1493.187

3.8373.8863.916

4.18

4.77 +0.03

0.107

0 232~

4.11

4.184.234.304.394.494.614.70

(2)(2)

0

0.055

0.0200.0080,0230.1600.0430.0130.033

20

4.89 ~0.03

5.02 +0.03

4.85

4.904.954.995.04

(o) 0.055

0.040

5.14+0.03

5,34 +0.03

0.067 '

5.335.445.575.645.745.805.86

0

(0)0

0.0800.133

0.0900.1650.0350.0600.0200.1200.045

1812 M. S. ZISMAN AND B. G. HARVE Y

TABLE II (Continued)

No.Levels

observed ~

(Mev)Intensity b

(mb)

Levelsobserved c, d

(MeV)

(3He, d)

ds'9'Mo(g.s.) decay

Levelsobserved'e

(Mev)

5.95+0.056.09 +0.05

(0 1) 0

Weak6.016.096.176.215 H

422

(4) n

0.5000.0750.103Qeakn

Excitation energy +20 keV except as noted. The Q value for the reaction was assumed to be -14.643 MeV (see text).Integrated from 0 I =12.5 to 57 except as noted.Excitation energy +15 keV.

d Taken from Ref. 2 except as noted. All E =2 levels up to 5.44 MeV are assumed d&&2. All l =4 levels except theground state are assumed g 7&2.

~ Taken from Ref. 17. Only those levels believed to be populated in the g.s. (~9+) decay are included. All energies+1 keV or less. The upper limit for the decay is about 4.4 MeV.

f Not resolved.&Integrated from 0~ ~ =12.5 to 52'."Taken from Ref. 4, All/ =1 levels except 0.103 MeV are assumedP3&2. The 1.85-MeV level is assumedf&&&.' Integrated from 8~ I =12.5 to 36.5'.j The existence of this level was uncertain."Integrated from 8 =12.5 to 42'.~ Taken from Ref. 1.

Integrated from 0 =12,5 to 42'."Taken from Bef. 6.

Observed at only three angles. The average differential-cross-section ratio to the 4.18-MeV level ( 0.9) was usedin obtaining the intensity.

of —0.319 MeV [using the published "Zr('He, d)

Q value], "which is considerably different fromthe value of -0.227~0.020 MeV reported in Ref. 6.A summary of the relevant Q values is given inTable I.

The change in the "Nb mass excess required byBall and Cates" and our own data'4 is about +95keV, which is slightly less than the value of +120keV indicated by the "Zr( p, n)"Nb data. " Perhapsthe discrepancy is due to an error in the "Zr-('He, d) and "Zr(u, t) Q values, "since the re-sults'+" from the "Zr target are only relative tothese numbers. However, the (n, t} calibration"is also consistent with the position of the "Zr-(u, t)93Nb(g. s.}peak which would mean that this

Q value" must also be in error in order to agreewith the results of Ref. 13. Based on these re-sults, we feel that the "Zr('He, d)"Nb Q value de-termined in Ref. 6 is incorrect. The '0Zr(n, t)"Nb

value used in our analysis is -14.643 MeV. Thiscorresponds to the relative difference in (n, t) Qvalues of 680 keV discussed above, and is slightlyless negative than the value of -14.665 MeV whichwould be inferred from the "Zr( p, n)"Nb results. "

The excitation energies of "Nb states observedin this work are given in Table II. The resultsagree, in general, with those of Vourvopouloset al.' and indicate that the excitation energies re-ported by Picard and Bassani' and Knopfle et al.'are somewhat too high. Of course, our method of

calibration gives excitation energies that dependon the choice of Q value for the 90Zr(n, t) reaction.If the Published 90Zr(n, t} Q value" is used, the ex-citation energies correspond rather well to thoseof Ref. 6. The errors quoted in Table II reflectan uncertainty of +27 keV in the Q value used inour analysis, but must be considered in the con-text of any redetermination of this value.

A triton spectrum of the reaction ~DZr(o, , t)"Nbat 0, =30'is shown in Fig. 1. The resolution is50 keV, full width at half maximum (FWHM). The

g, &, ground state is a factor of 15 more intensethan any other single level in the spectrum. In the'0Zr('He, d)"Nb data at 30.9 MeV' the ground statehas only about -', the intensity of the 3.36-MeV l=2level. Based on the strength of the ground state(g,z), the spectroscopic factors from ('He, d)"indicate that cr„,+/o, z+ = 5 for the (n, t) reaction.

Figures 2 and 3 show angular distributions oftritons leading to some of the stronger final states.The angular distributions of all strong triton groupsshow very little structure. One observable differ-ence between the I =4 (g.s.) and I=2 (3.37 MeV)curves, displayed in Figs. 2 and 3, respectively,is the forward-angle behavior: The 1 =2 curvetends to flatten out near 10', while the I, = 4 curveis much steeper. The 4.77-MeV level, assignedI= 4 by the "Zr('He, d) reaction, "also shows avery steep angular distribution at forward angles(see Fig. 2). The 4.18-MeV level, whose angular

HIGH-SPIN -PROTON STATES OBSERVED IN. . . 1813

200 I I I I S I I I I I I I

F (O.O)

I GO-Ea = 50 MeV

eg" 30'8000 F, C

I20-

N (00)eo-

ZO24 pig

2I l2~3 ZZ

40- IOy

l IIII,I f I

L

,400 500 600 700 800 900Channel

FIG. 1. Triton energy spectrum from the reaction9 Zr(&, t)9 Nb at 0, =30'.

distribution is shown in both Figs. 2 and 3, hasbeen assigned" 3 =2 (the I value is bracketed inRef. 2). The (n, t) angular distribution agreesbetter with the l =4 curves, although the differencesare very slight.

A more serious discrepancy with the l = 2 as-signment of the 4.18-MeV level comes from thestrength of the state. The spectroscopic factorsgiven for this level predict it to be weaker thanthe 3.37-MeV level by a factor of between 14 (Ref.6) and 20 (Ref. 2), while the relative cross sec-tions of the levels seen in the (o., t) data (Table II)

show a difference of only a factor of 2. Thus, the4.18-MeV level is between 7 and 10 times toostrong to be consistent with the /=2 spectroscopicfactors of previous work." This discrepancyseems rather large, since it has been verified"that (n, t) spectroscopic factors are, in general,the same as those obtained from ('He, d) experi-ments (within about a factor of 2). Additional evi-dence for the existence of a high-spin state in thisregion comes from a recent study of the P decayof "Mo,"which indicates a weak level at 4.179~0.001 MeV. A summary of the levels observedin the P decay is included in Table II. Since nointensity is given for the y decay of the 4.179-MeVlevel, it is not possible to distinguish between anallowed and a first-forbidden electron-capture de-cay. For an allowed decay, final spins of —,", &',or '-," are possible, and for a first-forbidden tran-sition —,', &, -', , &, or & states are permit-ted. The shell model rules out the &', &, and

possibilities, since the level is strongly popu-lated in proton transfer. A & assignment seemsunlikely because the 4.1'?9-MeV state is observedto decay only to the -,'ground state. ' There areat least two ~ levels and a number of T levelswhich should be fed from the decay of a & state,while none are observed. A & level stronglypopulated by the (ct, t) reaction wouM presumablybe an f», proton-hole state. However, in the avail-able (d, 'He) experiments in this mass region' "

1.0 I.O

eV

MeV

O.I— OI:

MeV

4.18

X

0.01— 0.01—

4.1 8 MeV

0.0 Mevx I

80

0 10 20 50 40 50 60 70 80 908, (d g)

FIG. 2. Angular distributions of tritons from the reac-tion 90Zr{n, t)9 Nb leading to the 0.0-, 4.18-, and 4.77-MeV levels. Statistical errors are shown for each point.The curves have no theoretical significance.

0 IO 20 30 40 50 60 70 80 90

( deg )

FIG. 3. Angular distributions of tritons from the reac-tion 90Zrj'0.', t)~ Nb leading to the 3.37- and 4.18-MeV lev-els. Statistical errors are shown for each point. Thecurves have no theoretical significance.

M. 8. Z ISMAN AND B. G. HARVEY

500 I. I I I I I I I I

IIF(0.0)

400- Eu= 50 MeV1

e~= l5

4000 p, C

I6

18

QQ, I R

I OO-

Vl '

c 200-

I I I

000 500

IO

AII1J600 700 800 900

FIG. 4. Triton energy spectrum from the reaction92Mo(0,', t)93Tc at 0& =15 .

no f», hole states were observed. The remainingchoices»", ~', and & are all equally consistentwith the p-decay results. "

The 4.89-MeV level observed in the {u, f) experi-ment corresponds to an unassigned doublet at 4.85and 4.90 MeV in Ref. 2. A level at 4.912 MeV wasobserved in a lower-energy experiment' and as-signed 1 =2. The (u, f) angular distribution of the4.89-MeV level (not shown) corresponds moreclosely to the I = 4 shape and the strength of thestate is too large re1.ative to the 3.37-MeV levelby a significant factor. The spectroscopic factorfor this level w'ould correspond to a cross sectionrelative to the 3.37-MeVlevelof 1/16instead of theobserved intensity ratio of 1/2. 3. Thus, the 4.89-MeV level is 7 times stronger than its L= 2 assign-ment' would indicate. Unfortunately, the P decayof "Mo(T )"can only populate "Nb levels up toabout 4.4 MeV so it provides no additional infor-mation about the 4.89-MeV state.

In the excitation-energy region between 2.5 and3 MeV there are several levels observed in (u, f)which appear esther weakly"' or not at all' in the('He, d) data. The many levels which are populatedby both reactions make it seem likely that these"new'" proton levels, e.g., 2.30, 2.39, 2.53, 2.61,2.7V, 2.90, and 3.01 MeV, appear in the 'OZr(u, f)-"Nb spectrum because they are high-angular-mo-mentum transitions. The large value of Q xR (=6)for the (u, f) reaction favors 1=4-6 transfers,while the ('He, d) reaction has the best momentummatching for / = 2-3 transitions. Thus, states con-taining small amplitudes of, say, g,I„g„„orh»» strength would have larger cross sections in

(u, f} than in ('He, d). Of the six levels seen in the

(u, t) experiment between 2.39 and 3.01 MeV, onlythe 2.90-MeV level was not reported in the P-de-cay study. " This supports our contention thatthese levels are high-spin states having at least

some single-particle amplitude.The 5.14-MeV level seen in (u, f) has an intensi-

ty relative to the 3.37-MeV level of about 1/3. Ofthe reported" levels in this region, only that at5.24 MeV has a spectroscopic factor consistentwith the intensity ratio from (u, t}. However, thediscrepancy in excitation energies between the(u, f) and ('He, d) states is larger than the expect-ed uncertainties, if both reactions are populatingthe same level.

The intensity of the 3 =4 level near 6 MeV seemsrather low in the (u, f) data compared with the('He, d) spectroscopic factors."Kn6pfle ef alshow a cross-section ratio o(6.04)/c(4. 82) ~ 2,while our data give o(5.95)/c(4. 77) = 1/2. Unfortu-nately, the 6-MeV region of the spectrum is ob-scured at forward angleS by the '7F(g.s.) impuritypeak, so the measured intensity of the 5.95-MeVlevel is only approximate. Whether the apparentdifference in strength is related to the fact thatthe upper level is slightly unbound cannot be de-termined without distorted-wave Born-approxima-tion (DWBA) calculations.

The appearance of probable high-angular-mo-mentum transitions at 2.39, 2.53, 2.61, 2.77, 2.90,3.01, 4.18, 4.7"I, 4.89, and (5.14) MeV is consis-tent with the general picture of the proton statesin "Nb. It w'as pointed out in Ref. 2, for example,that the number of g„, levels observed is muchsmaller than expected compared with the consider-able fragmentation of the I,=0 and (=2 levels. How-ever, the two observed' I =4 transitions (at 4.80and 6.01 MeV) already account for over 90'jj~ of thetotal g», strength so the appearance of these "ex-tra" levels w'ould require a renormalization of thespectroscopic strength if some of them are, infact, g», fragments. Of course, another possibleexplanation for the strong levels in (u, f) is thatthey contain h»~ fragments. In this case our re-sults would not be in contradiction with those from('He, d) 2

8. Mo(0{, t) Tc

A triton spectrum of the reaction "Mo(u, f)93Tc

at g, = 15' is shown in Fig. 4. The resolution is55 keV {FWHM). The intensity of the ground state(g») is again much greater than that of any otherlevel in the spectrum. A summary of the levelsobserved in the reaction "Mo(u, t)93Tc comparedwith the "Mo('He, d) results' ' is given in Table III.The spectra were calibrated using the '~ (F. g}sand"Tc(g.s.) peaks as a function of angle, with Q val-ues obtained from Ref. 11. As can be seen fromTable III, the excitation energies determined inthis work agree well with those found previously, ' 'with very few exceptions.

HIGH-SPIN PROTON STATES OBSERVED IN. . .

The largest energy discrepancy occurs for the(o., t) level at 3.10+0.02 MeV, which may corre-spond to the ('He, d) state observed at 3.1V0~0.02'and 3.14V+0.015' MeV. However, the /=2 spec-troscopic factor for the 3.147-MeV level is only

~ that of the 3.343-MeV level, ' while the (o., t) in-tensity ratio, o(3.10}/&r(3.36), is about 1/4. Thus,the different values for the excitation energy maybe due to population in (n, f}, but not in ('He, d), ofa high-spin state near the 3.16-MeV level.

The 0.68- and 2.14-MeV levels, both weakly pop-ulated in ('He, d}, are relatively stronger in (o., t),which indicates high-angular-momentum assign-

ments. The 2.13-MeV level was assigned l =3(f») in Ref. 6, in agreement with the strongerpopulation in (tt, t). The 0.68-MeV state, which isquite weak even in (o., t), might correspond to a &level calculated to be at about 0.7 MeV in "Tc.'""Population of this level, which is mainly a(sg„,)'v„+ configuration, would indicate some mix-ing with the ng», single-particle state.

In the QsMo(n, t)"Tc spectra, as was the casewith "Zr(a, t)"Nb (see above), there is one level,at 3.91 MeV, whose strength is inconsistent withthe 1=2 assignment' from the ('He, d) reaction.(The 3.890-MeV level is also given a tentative I = 2

TABLE III. Levels observed in the reaction 92Mo(e, t)83Tc at 50 MeV.

No.Levels

observed ' Intensity ~

(Mev) (mb)

Levelsobserved Ip

(MeV)

Levelsobserved

(Mev)

('He, d) b

16171819

20

0.00.390.681.181.42 +0.03

1.511.782.142.59+0.043.10

3.363.583.91

4.15+0.044.37

4.474.67 +0.034.77 +0.034.90

5,20 +0.03

6.01+0.036.17+0.036.44 +0.04

3,7090.1180.0400.0190.037

0.044o.o55'0.0970.0820.091

0.3900,0640.245

O.O59'O.192'

o.o66"o.ov'O.O8V'

0 166i

O.O9V"

O.16"0 lvhO.ll"

0.0 40.390 +0.010 10.660 +0.0201.190 +0.015 1

1.500 +0.015 11.780 +0.020 12.130 +0.0202.565+0.020 2

3.1vo ~0.020 (2)3.360 +0.020 2

3.910 +0.020 24.110+0.020 (0)

4.794,925.025.18

5,335.495.65

0.670.30Weak

0.03, 0.01

0.10, 0.040.12, 0.05

Weak0.04, 0.02

0.78, 0.38

0.09, 0.05(o.15)

0.00.396+0.005(0.66)1.21 +0,020

1.500+0.010 11.788 +0.010 12.134+0.015 32.556+0.015 2

3.147 +0.015 23.343+0.015 2

3.89 +0.020 (2)4.09 +0.030 0

4.39 +0.040

4.76 +0.0304.88 +0.030

5.170 +0.015 1

5.302 +0.015 25.5o ~0.040 (2)5.64 +0.040 25.98 +0.040 (5)6.24 +0.040

0.500.28Weak

0.034, 0.015

0.12, 0.0520,11, 0.048o.o45 g

0.037, 0.019

0.034, 0.0180.78, 0.41

(0.11, 0.06)0.23

0.23, 0.083

0.059, 0.032(0.051, 0.028)0.035, 0.019

(o.ov9) ~

Taken from Qef. 1. No spectroscopic information is given for levels above 4.110 MeV."Taken from Hef. 5.Excitation energy +20 keV except as noted.Integrated from 8 =12.5 to 57' except as noted.

~When two values are listed the first corresponds to j=i —~z, the second to j=i+ /.Integrated from 8 I =12.5 to 52 .

& Assumed f&&2.

"Integrated from 8 =12.5 to 36.5'.' Integrated from 8 ~ =15.5 to 52'.j Assumed A, &&&2.

M. 8. Z~SMAN AND B. G. HARVEY

assignment in Ref. 5, although it does not have atypical 1=2 angular distribution. This may be anindication that there exist two closely spaced lev-els at this energy but Kozub and Youngblood5 foundno combination of two E values which would yieldthe observed shape. ) The angular distribution ofthe 3.91-MeV level (Figs. 5 and 6) shows a forward-angle behavior similar to that of the ground state(I = 4); it does not appear to flatten out at forwardangles as does the 3.36-MeV level in "Tc (and the3.37-MeV level in "Nb). As mentioned above, thisdifference in angular distributions is very slightand would certainly not allow a determination ofthe j transfer by itself. The spectroscopic factorsfor this level from the ('He, d) experiments' ' pre-dict it to be weaker than the 3.36-MeV level by afactor of about 7, while the ratio of (n, t) crosssections is about 1.6. The 3.91-MeV level ob-served in the "Mo(o., f) data is, therefore, aboutfour times too strong to be consistent with the 1=2assignment of previous work. "

Around 4.5 MeV there are several levels (mostlydoublets) which are more strongly excited by (a, f)than (He, d).' ' Thus they may be populated byl &2 transfers. The angular distributions of the4.3'I- and 4.90-MeV states (Fig. 5) are similar tothat of the l =4 ground-state transition. Moreover,Vourvopoulos eI; al.2 found /=4 levels at about thisexcitation energy in "Nb,

The 5.98-MeV level seen in Ref. 5 probably cor-

responds to the multiplet at 6.01 MeV in the (n, t)data. The tentative l = 5 assignment made by Kozuband Youngblood5 for the 5.98-MeV state is in quali-tative agreement with the observed strength of the6.01-MeV multiplet in (n., t) (see Fig. 4). The('He, d) experiments finds the d», analog state at8.4 MeV, which corresponds to a splitting betweenT& and T& centrolds of about 4.7 Mev for the d5/2configuration. Recent "Mo(d, p)"Mo experi-ments'~" show the existence of an @x„2 neutronlevel at 2.30 MeV. Assuming the same splittingbetween T& and T» states for the h»„configura-tion in "Tc would then give 6.0 MeV as the expect-ed location of the T& 3=5 levels. The predictedg», centroid would be about 5.2 MeV (based on theneutron single-particle centroid from Ref. 20), butthis is somewhat higher than the strong levels ob-served in our data. The data of Vourvopoulos eta3.2 indicate that the T&-T& splitting is about IMeV larger for the g» states than it is for thed, ~, states in "Nb and a similar difference in "Tcwould predict a gv&2 centroid in reasonable agree-ment with the observed strong levels in "Tc be-tween 3.9 and 4.9 MeV.

It is interesting to note that the 90Zr(d, p) and

(n, 'He) reactions" find the g„, and h»„centroidsat the same energy in "Zr, which would suggest theexistence of T& 1=5 states near 5 to 6 MeV in "Nbas well as "Tc, although none have been observed.[The 6-MeV levels observed in "Nb are not as

I,O

0 MeV MeV

437MG. I—X 4

O. I—

4.9OOI: x

0 MeV x20G.OI— 3.56 MeV

39l MeV x—2

3.9l MeV x —'2

IO 20 BG 00 50 60 70 80 906' (deg)

FIG. 5. Angular dist1ibutlons of trltons from the 1eac-tion 92MO(0, , t)93Tc leading to the 0.0-, 3.91-, 4.37-, and4.90-MeV levels. Statistical errors are shown for eachpoint. The curves have no theoretical significance.

0 I 0 20 30 40 50 60 70 80 90

8, (deg)

FIG. 6. Angular distributions of tritons from the reac-tion 92MO(0,', t)93Tc leading to the 3.36- and 3.91-MeV lev-els. Statistical errors are shown for each point. Thecurves have no theoretical significance.

HIGH-SPIN PROTON STATES OBSERVED IN. . .

strongly excited with (u, f) as those in "Tc andhave been assigned l =4 by the (He, d) reaction. a']

IV. CONCLUSIONS

The reactions '0Zr(u, f) and "Mo(u, f) have beenused to search for high-spin (I &2) levels in "Nband "Tc. Based on relative intensities of levelsseen in both the ('He, d) and (u, t) reactions, O'Nb

states at 2.39, 2.53, 2.61, 2.77, 2.90, 3.01, 4.18,4.77, 4.89, and (5.14) MeV are probable candidatesfor levels with E =3, 4, or 5. The 4.18-MeV levelis assigned I = 2 from ('He, d),' ' but the large (u, t)strength and P decay of 9'Mo(T )"indicate a highspin for this level. Levels near 6 MeV appearrather weakly in (u, t) although a strong / = 4 levelwas observed in the (He, d) experiments" at 6.01MeV. From the position of the A»» neutron cen-troid in "Zr it is expected that 3 = 5 proton levelsmay also exist: in the 5- to 6-MeV region of "Nb,which could provide an explanation for some of thestronger levels observed in the (u, t) data in thisregion.

Possible high-spin levels in "Tc include the 0.68-,

(3.58-), 4.37-, (4.47-), (4.67-), 4.77-, 4.90-, 6.01-(multiplet), 6.17-, and 6.44-MeV states .The statesabove 6 MeV may be l=5 levels based on tentativeresults from the ('He, d) experiment of Kozub andYoungblood. ' The 3.91-MeV level, assigned k = 2from the ('He, d) studies, "is populated toostrong-ly in (u, f) to be consistent with the measuredspectroscopic factors and is believed to have E &2.

The Q value used in our analysis of the reaction90Zr(u, t)"Nb, -14.643 MeV, corresponds to achange in the ~'Nb mass excess of +98 keV. Thischange is roughly consistent with a new Q valuedetermined for the "Zr(p, n) reaction" but con-tradicts a recent measurement of the Zr( Heq d)-"Nb Q value' which confirms the "Nb mass excessof Mattauch, Thiele, and Wapstra. "

V. ACKNOWLEDGMENTS

We thank J. D. Sherman for his help with theexperiment and C. Maples for allowing us to usehis computer code LORNA for some of the dataanalysis. %e also are indebted to C. Ellsmorthfor preparing the targets.

*Work performed under the auspices of the U. S.Atom-ic Energy Commission.

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Calculations were made with the data analysis pro-gram LORNA written by C. Maples.

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