PHYSICAL R EVIEW C VOLUME 13, NUMBER 5 MAY 1976

Recoil-distance lifetime measurements of states in 47V and 47Ti

induced by heavy-ion reactions

M. Toulemonde, N. Schulz, l. C. Merdinger, and P. EngelsteinCentre de Recherches Nucleaires et Universite Louis Pasteur, Strasbourg, France

(Received 13 November 1975)

The recoil-distance method has been used in conjunction with heavy-ion reactions to measure the following

mean lives: 7 = 1.23 +0.16 and 0.63 +0.13 ns for the 88-keV 5/2 and 146-keV 7/2 states in "V, and

r = 314+22 ps for the 160-keV 7/2 state in "Ti.

NUCLEAR REACTIONS P( F,P2ny)( SF,n2Py) E =47 MeV; measured recoildistance. TV, Ti levels deduced T&/2, B(~1),B(E2). Natural target, Ge(Li)

detector.

I. INTRODUCTION

Evidence for deformation of the even-even nu-clei in the middle of the 1f,~, shell already exists.The energy of the first 2+ states decreases fromthe nuclei with doubly closed shells towards thecenter of the sheQ and the strength of the corres-ponding (E2, 2'- g. s.) transition increases. ' Lessinformation is available for the odd-A nuclei.Among them, "V represents a very peculiar casebecause it is the only nucleus in this region knownto have a ground state with spin and parity & .This feature is not reproduced by simple (If,~,)'calculations, whatever two-body matrix elementsare used. ' Recently spin assignments, branchingratios, multipole mixing ratios, and lifetimes forlow-lying levels of "V have become availablemainly through the studies' ' of the "Ti (P, ny)and "Ca ("B,n2Py) reactions. In the presentwork, the lifetimes of the two first excited statesof "V are measured with the recoil-distance tech-nique in the "P ("F,P2n) reaction. In addition, aprecise value for the lifetime of the first excitedstate in "Ti, populated via the "P("F,n2P) re-action, is obtained.

II. EXPERIMENTAL ARRANGEMENT

AND DATA ANALYSIS

Lifetimes were measured with a plunger appar-atus similar to the one described elsewhere. 'The target consisted of a 250-pg/cm' thick lays~of Zn, P, evaporated onto a 1-mg/cm' thick Au

foil. A thicker circ~~r Au foil, of 5.2-cm dia-meter, was used to stop the recoiling nuclei. A47-MeV "Fbeam from the MP tandem Van deGraaff was used to populate the levels of interest.The y-ray spectra were measured with a 3.1-cm'Ge(Li) detector at 0' with respect to the beam.

Under actual running conditions, the resolutionwidth of the Ge(Li) detector was 1 keV for a 88-keVy-ray line.

Since in the present experiment the recoil dis-tances D were not always negligible compared tothe target-detector distance, the variation of thesolid angle had to be taken into account. Thephotopeak efficiency of the counter versus dis-tance x from the source was determined by usingthe 81-keV y ray of "'Ba. Following the methodoutlined by Goosman and Kavanagh, ' the numbersof counts versus ~ were fitted by a function AeA being a constant. A value of n = 0.220+ 0.011cm ' was obtained from this fit.

The y-ray data for the 160-keV transition in4'Ti are shown in the left half of Fig. 1 for threetarget-stopper distances D= d —d„d being thereading of the micrometer which positions thestopper and d, the reading for zero target-stopperdistance. The peak areas I, and I, for the un-shifted and shifted lines were extracted fromthese spectra by subtracting an exponential back-ground. The area of the shifted component hasto be corrected for the energy dependence of theGe(Li) detector efficiency and for the large solidangle due to the nuclei's motion. The two effects,which are of opposite sign, cancel to within 1% inthe present experiment where a mean recoil ve-locity v = 0.0268c is determined from the differ-ence in centroid energies of the two components.A small background in the unshifted component isobserved at large D distances. If this backgroundis due to cascade feeding from a long-lived levelor from radioactivity on the stopper, the area I,may be expressed as:

I,= N(exp [ (D/v7) (1 —ave)-]+ Ce~),

where r is the mean life of the level under studyand N a normalization constant for each value of

13 1889

1890 TOULEMONDE, SCHU LZ, MERDINGER, AND ENGE LSTEIN

1100 0 004I

~ooI

1.0-160

I I

7/2

800-

500-

0 =2.70

~ y~ ~h ~~+~& ~o

~ ~,~ '~ ~~oA op» o,'~qao ~ ~o

]o1300- ~ o

Io o~ ~~ ~

~ ~ ~

~0

CA +o~p o S W 'o oo1~ ~ ~I

700-0 =7.70

~ ~ ~v ~

~ So~

~ +'Co ~1600-

~,W~o

C'

1000- ~ ~

~ ~ ~ op g ~ooo~ ~ ooooO ~'ls

~ ~~ oy oo ~

00.1-

0 ~7' 5/2"Ti

1950 2000

CHANNEL NUMBER

1300-~ ~ eo ~oo ~

~ ~ r~ ~ ~ ~ op ~ 0 ~ oo ~ ~ ~ ~ ~ o\ ~~ o ~ ~~ ~ ~ ~ oooo eyyy~ ~ ~ oo ~ ~ ~ ~ ~

A oooo ~

~ ~1000-2050 10

I

20

0 (mmj

I I

30 50

FIG. 1. Recoil-distance data for the 160-keV g.s. y transition in 47Ti. The left portion of the figure displays yspectra taken at three different plunger distances D(mm). The right portion of the figure is a semilogarithmic plotof 10/(10+I~) versus D. The solid curve represents the best fit of Ep. (4) to the data.

D. In the present experiment, comparable yieldsfor the n2P and P2n evaporation processes wereobserved. Since only 0.1/o of the P decay' of "Vis feeding the 160-keV level in "Ti, this may notbe the main process producing the background. Ifit is supposed that background is due to the y ra-diation from a level whose lifetime is short corn-pared to the transit time of the ion in the target

material, the quantity Ce in Eq. (1) has to bereplaced by a constant. The peak area I, is givenby Eq. (3):

I, =N/1 —exp[-(D/vv') (1 —nvv)]] /(1 —av7)

and the sum of both peaks areas by Eq. (3):

f, +f, =g((1 —nvv exp[-(D/vT)(1 —ave)]}/(1 —ave)+Ce ). (3)

The experimental ratios of the unshifted area to the total area were fitted with the following formula:

f./(f. +f. ) = exp [-(D/v7) (1 —ave)) + Ce(1—avrexp[ (D/v7) (1 -—ave)])/(1 —ave)+Cev~ ' (4)

d, =d-D, ~ and C being the free parameters. Thesolid curve in the right half of Fig. 1 correspond-ing to 7 = 314+ 22 ps represents the best fit forthe 160-keV level in "Ti. This lifetime value isin agreement with the values v=320+ 100 ps andv = 294+ 24 ps obtained by direct timing. "

Only the unshifted peak for the 146- 88-keV ytransition in '7V was analyzed, due to the pres-ence of another strong line in the y spectrum nearthe shifted peak. For each plunger setting, thearea of the unshifted peak was normalized by theconstant N which was deduced from the "Ti dataand Eq. (3). The normalized areas were fittedwith the following formula:

I,= K (exp[-(D/vr, ) (1 —ave, )]+C, e~),

where K is a normalization constant independentof D. The value found for d, by fitting the "Tidata was taken as a constant and only three freeparameters were left: K, 7y and C,. The decaycurve for the 58-keV y transition is shown inFig. 2. The fit to the data yields a value of 7,= 630+ 130 ps.

The x-ray peaks from a Pb impurity were ob-served in the y spectra. The K(P, ) line is clearlyseen in the left side of Fig. 3 which displays they-ray data for the 88-keV transition in "V forthree plunger distances D. The peak in the mid-

RECOIL-DISTANCE LIFETIME MEASUREMENTS OF STATES. . . 1891

1.0

7/2

TABLE I. Experimental and theoretical transitionprobabilities in 47V.

Trans itioncharacter

Reduced trans ition probabilitiesExp. Calc. A Calc. B

2 2

7 52 2

7 3.2 2

M1 (]tf,z~)

&2(e fm)

0.07 + 0 ~ 01

0.45+ 0.09

315+ 118

0.01

0.02

41

0.07

0.07

78

CfJ

0~C

0.1—259-keg level whose mean life' is 90 ps. Ignoringthis small contribution, the normalized intensitiesI, were fitted by the following formula:

&, = K'(7, {1—exp [ (D/vr, )-(1 —«r, )]) /(1 —«&,)

—r, [1—exp[ (D/vr, ) -(1 —ovr, )])/(1 —nvT, ))

(8)I

10

0 (mm}

FIG. 2. Decay curve for the 146-keV 88-keV p tran-sition in 4~V. The solid curve represents the best fit ofEq. (5) to the data.

die of the spectra is composed of both the un-shifted 88-keV y ray and the K(P,) line from Pb.Therefore only the shifted component I, was ana-lyzed. The feeding of the 88-keV level was al-most completely due to the 58-keV y transition.Only a few percent of the feeding arose from the

where the indexes 1 and 2 refer to the 146- and88-keV levels, respectively. A first fit with K',~„and v, as free parameters, yielded values of7, = 645 ps and 7, = 1.20 ns. A second fit with onlyK' and 7, as free parameters yielded a value of7, = 1.23+ 0.16 ns.

The errors on the lifetimes include possibleerrors due to deorientation effects. These addi-tional errors, whose maximum values rangedfrom 2 to 5%, were evaluated using Eq. (23) fromRef. 10. The parameters A.~ and A~ of this equa-tion were determined in the same way as Browne] g)."

200- t

D = 0.041600-

% ~\ ~

1200-

D= 7.70

K~

2800-~ M

8 ~ ~

~ ~ yt

2f00- '.'. "

~ ~

lo+ K&

«~ea+ ~, S ~ e el V ~8 ~ ~ ~ '~ ~~ ~ ~ O, ~ ~

] 5

0.1—

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5/2

2000-

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A~ r

~ e ~

~ re~~ ~~~ ~ q ~ ~ ~

~ ~

88

0 a' 3/2

2000 ~ ~ ~ ~ ~ oo

l ~

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I

1050 1100

CHANNEL NUHBER

a ~ ~~ a~ %r Nr ~ re ~

1150I I I

10 20 30

0{me)

50

FIG. 3. Recoil-distance data for the 88-keV g.s. p transition in 4~V. The left portion of the figure displays p spec-tra taken at three different plunger distances D(mm). The x ray lines are due to a Pb contaminant. The right portionof the figure is a semilogarithmic plot of I, versus D. The solid curve represents the best fit of Eq. (6) to the data.

1892 TQULEMONDE~SCHULZyMERD INGER)AND ENGELSTE IN

III. CONCLUSIONS

Mean lives of T = 1.23+ 0.16 ns and 7 = 0.63+ 0.13ns for the 88-keV 2 and 146-keV ~7 states in"V are obtained in the present work. It should benoted that the lifetime value for the 88-keV stateis in slight disagreement with an earlier upperlimit of 1 ns obtained by the pulsed-beam tech-nique in the "Ti (P, ny} reaction. ' Table 1 sum-marizes the reduced transition probabilities de-duced from the present work. The dipole char-acter of the 2 - 2 transition is known from aconversion coefficient measurement. " The

E2 transition strength is obtained by usingthe experimental branching ratio' of 0.016+ 0.005for the 146-keV level to ground state decay. The

Ml transition rate is calculated assumingthat the corresponding B(Z2) & 100 W. u. (Weiss-kopf units).

It has been shown in a previous work' that where-as the 1f,~,

' picture (calculation A} fails to re-produce the excitation energies of the low-lyingnegative parity states, a dramatic change occurswhen 1f,~,

' (2P,~, 2P,~, 1f,~,) configurations (cal-culation B}are also allowed. The same trend isobserved for the calculated transition probabilitiesreported in Table I. It will be discussed in aforthcoming paper devoted to a detailed shellmodel study covering 1f,~, conjugate pairs, in-cluding '~V and "Cr."

The authors would like to express their appreci-ation to R. Freeman for stimulating comments.

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