Isoscalar and isovector M4 spin transitions in 14C

Volume 137B, number 1,2

PHYSICS LETTERS

22 March 1984

ISOSCALAR AND ISOVECTOR M4 SPIN TRANSITIONS IN 14C M.A. PLUM, R.A. LINDGREN, J. DUBACH, R.S. HICKS, R.L. HUFFMAN, B. PARKER, G.A. PETERSON University o f Massachusetts at Amherst

1, Amherst,

MA O1003, USA

J. ALSTER, J. LICHTENSTADT, M.A. MOINESTER Tel Aviv University 2, Tel Aviv, Israel 69778

and H. BAER Los Alamos National Laboratory, Los Alamos, N M 87545, USA

Received 9 December 1983

Inelastic electron scattering cross sections, measured for 14 C j ~ - = 4 - states at 11.7, 17.3, and 24.3 MeV, have been combined with previously measured (n, #) cross-section ratios to deduce the isoscalar and isovector amplitudes of the spin transition densities. The T = 1 states exhaust (33-45)% of the isovector single-particle strength, and (1-15)% of the isoscalar strength. Pion scattering cross sections for the T = 2, 4 - state at 24.3 MeV are predicted.

In general, (e, e') magnetic transitions depend upon the coherent sum of isoscalar and isovector spin and orbital transition densities [ 1 ], while corresponding (n, n') cross sections depend solely upon the spin densities. However, for a "stretched" transition [2], the orbital transition density is zero and only the spin contributes in (e, e'). In non-self-conjugate nuclei, where both isoscalar and isovector spin densities can contribute to transitions between states of the same isospin, the contributions of each component cannot be determined from (e, e') data alone. Nor can they be determined from (n, n') data alone, without having to rely upon an absolute calculation of the inelastic pion-nucleus differential cross section [3]. In this letter, it is shown for the first time how measured (e,e') cross sections can be analyzed together with measured (n, Tr') cross-section ratios to determine the i Supported by the US Department of Energy. 2 Supported by the US-Israel Binational Science Foundation, BSF-Jerusalem. 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

individual isoscalar and isovector amplitudes of the spin transition density p}. Each amplitude can now be individually compared with shell model predictions, and can be used to help separate the effects due to nuclear structure from those due to the reaction mechanism in studies of hadron scattering. To this end, (e,e') cross sections have been measured for the A T = 0 and AT = 1 M4 transitions in 14C. In the course of these studies, evidence has also been found for a previously unobserved T = 2, J ~ - - 4 - state at 24.3 MeV. The (e, e') data were taken at 180 ° at the Bates Linear Accelerator using 100 to 300 MeV electrons. About 80 mg/cm 2 of radioactive 14C powder was contained in a target cell with 0.025 mm stainless steel foil windows, which in turn was enclosed in a containment cell with 0.0064 mm Havar foil windows for additional target integrity. Analysis was performed using standard techniques [4]. Because 12C was present in a 12C/14C atom ratio of 0.219 -+ 0.018, cross sections were obtained by normalizing to known 12C peaks [5]. This letter concerns the three prominent 15

Volume 137B, number 1,2

PHYSICS LETTERS

22 March 1984 24.5 4 -

io

14C ( e , e ' ) E0 " 1 9 6 . 5 M e V

4.0

v

4i .7z

417.33

0 • 180"

E 0

;3.0

0 ¢,.) 0 1,.. 0

2.0

22.11 3-

673

.r

2* 7.01

2*

1053 1-

832 98,1 j

t

I

i

~

1.0

co ¢.)

o

5

I0

15

20

"

l

I

2' 5

Ex (MeV) Fig. 1. Spectrum of electrons of initial energy 196.3 MeV scattered through 180 °. 14C excitations at 11.7, 17.3, and 24.3 MeV shown in the (e,e') spectrum of fig. 1. The two peaks at 11.7 and 17.3 MeV m a y be associated with j , r = 4 - , T = 1 states seen in inelastic pion scattering [7]. In fig. 2, the (e,e') form factors for I

I

i4C (e,e')

I

I

( d5/2, p3~;)4:

~

1.54fm

0 O"

/:

10 -4

Ex = I I.?MeV'~

/;'

%,

0

E 0

//

'\

//E~: 17.3MeV'4

10 -4

L;

/J

i-

~,\

t

'~

) l/I tO

I--10-4

ff Ex-- 2 4 . 3 MeV

,/i I

I

I 2

q,ff

16

\}

-"

I

these transitions are compared to the results of planewave Born-approximation calculations for the singleparticle (d5/2, p~/1) M4 transition, the only possible one within a 1/~u~ shell model space. Harmonic oscillator wave functions were used with the parameter b = 1.54 fm and an overall form factor normalization determined by a least-squares fitting procedure. These two observed states can be associated with those predicted at 12.13 and 16.35 MeV in Millener's large basis shell model calculations [8]. Other negativeparity states predicted in this excitation region have form factors whose shapes are incorrect or inconsistent with the (lr,~r') data. The measured form factor for the 24.3 MeV state has a shape very similar to the form factor used to fit the 4 - , T = 1 states, especially at higher m o m e n t u m transfer q, thus supporting a 4 - assignment. It is consistent with the k n o w n [9] 14B 4 - , T = 2 state, the

(frn -I)

I

Fig. 2. Transverse form factor squared, F~, versus effective momentum transfer qeff. The solid curve includes MEC, and has been reduced in magnitude from the calculated values (see table 1). The dashed line shows only the one-body contribution. We use F~ = rl(do/d~)exp/[Z~M(1/2 + tan 2 (0/2)] where ~ is the recoil factor, (da/dS2)exp is the measured cross section, and aM = [~2 cos2(O/2)]/[4E2o sin4(O/2)] is the Mott scattering cross section. In PWBA, one has qeff = c/(1 + 3Zahc/2EoR), where R = [5/3(r2)] 1/2, and (r2) 112 = 2.496 fm, the rms radius of the ground-state charge distribution of 14C [6]. The error bars do not include an overall 8% uncertainty due to the 14C/12C atom ratio.

Volume 137B, number 1,2

PHYSICS LETTERS

14C analog of which is expected to lie at 24.2 MeV, suggesting an isospin assignment of T = 2. Shell model calculations [8] also predict a T = 2, 4 - state at 23.9 MeV. However, recent 14C(7r-,')') measurements [ 10] tentatively indicate a 2 - state in 14C at 24.3 -+ 0.1 MeV, corresponding to a known 2 - state in 14B. The shell model M2 form factor for this level is peaked at low q, suggesting that the analog of the 14B, 2 - state is unresolved and may be responsible for the enhancement of the (e,e') data below 1.3 fm -1. As shown in column 3 of table 1, the M4 form factors account for 41% and 37% of the T = 1 and T = 2 single-particle (e, e') cross section, respectively. Detailed shell model calculations [8] overestimate the data by a factor of nearly two as shown in column 5 of table 1. The contribution of meson exchange currents (MEC) [ 11 ], which scales approximately with the stretched p a r t i c l e - h o l e amplitude, increases the predicted (e,e') form factors by about 15% for both the simple p a r t i c l e - h o l e and the shell model wave functions, as given in columns 4 and 6 of table 1. After the MEC have been subtracted and the one-

22 March 1984

body densities determined, the electron data can be combined with existing pion data to decompose the T = 1 states into their isoscalar and isovector components. For inelastic electron or pion scattering to jTr = 4 - states in p-shell nuclei, the 'stretched' (d5/2, p3/12) matrix element should dominate the spin transition density. In this case, the cross section can be written in PWBA as

aT(X, x') o~ r=0,1 ~ ZrT Gr(x) p~q) 2 ,

(1)

where x and x ' are the incident and scattered electrons or pions, T is the isospin of the final state, and r = O(1) for an isoscalar (isovector) transition. The ZrT coefficients are spectroscopic amplitudes [12] ,1. In a pure p a r t i c l e - h o l e model for this transition in 14C, the "isoscalar transition strength", Z2T, has a maximum value of unity, and the "isovector transition strength", Z12T, is equally divided between the T = 1 and T = 2 states, with a maximum value of 1/2 for a given value of T; p~(q) is the one-body spin transition density

PXq) = (d5/21 [jj-l(qr)[Yj-l(O X o]JI 1P3/2), Table 1 Electron scattering cross sections for j~r = 4 - states in 14C compared to theoretical predictions with and without meson exchange currents. The errors do not include the overall uncertainty in the 12C/14C atom ratio. Ex a) (MeV)

T

°expb) × 100% asp

Oexp c) × 100% Othy

without

with

without

with

11.7 17.3

1 1

19-+ 1 22-+1

16-+1 19-+1

59-+3 63-+3

51-+3 53-+3

24.3d)

2

37-+7

32-+6

42-+8

36-+7

a) Estimated uncertainty in excitation energy is 0.1 MeV. b) The Oexp are the experimental cross sections at the peak of the fitted form factor, and asp are the calculated cross sections at the same q, assuming the maximum (ds/2, p~-/~) M4 transition strength to T = 1 or T = 2 states. At 180 ° Oexp = (2.55 nb/sr)[ZoTGo+Z1TG1] 2, and excluding MEC, Osp(T) = (2.55 nb/sr)[(1 - (-1) T) G2/2 + G~/21. Note that trexp/Osp is a reaction dependent quantity for T = 1 states in 14C. c) athy are the predictions of MiUener [8]. d) Estimated uncertainty in M4 strength for this state is 20% due to unknown contamination from a nearby state of lower spin.

which we assume to be independent of isospin. For electron scattering, GO (G1) = 0.440 nm ( - 2 . 3 5 3 nm), the isoscalar (isovector) magnetic moment, while for pion scattering, GO (G1) is the isoscalar (isovector) component o f the pion-nucleon scattering amplitude. Near the N* (3,3) resonance, G1/Go is roughly constant and equal to - 1 / 2 (+1/2) for rt+ (rr-) scattering [13]. If the bare values of these couplings are renormalized, then the effect will be reflected in the deduced Z-coefficients. It is assumed in the present analysis that such renormalizations are small, or, at least, reaction independent. Thus, assuming that distortion and absorption effects cancel, the ratio of rr+ to 1rcross sections for a stretched M4 T = 1 to T = 1 transition takes the simple form ,1 The Z-coefficients are related to the one-body transition density matrix elements qjjfi: fi ZrT = (-1) Ti-MTi( TMT Ti -MTil r Mr) qJjr/(Zli+ 1) 1/2,

fi = (JfT [ll[a~ds/2 Xapa/2]JrlllJiTi)/(2r+ 1)1/2(2j+ 1) 1/2. ffJz All non-essential indices on the Z-coefficients have been suppressed. 17

Volume 137B, number 1,2

PHYSICS LETTERS

22 March 1984

Table 2 Results for the Z coefficients and the relative (rr,n r) T = 2, j~r = 4 - cross sections. Ex 11.7 17.3

T 1 1

J 4 4

Ol(n+, 7r+,) a) al(~r-,~-') <1/17 >11

Zo 1

Zll

0.092 ~
0.30 ~
a2(n-,n-')

a~(n+,zr+')

°1(~-,~-')

al(~+,~ +')

0.15 ~
2.59 <~o2/01

2.28<~o2/a 1

0.21
a) Values from ref. [7].

Ol(rr+,zr+') Ol(Tr-,Tr-')

I2(Zo1/Zll ) -- 112 I2(Zo1/Zll ) + 112,

(2)

and determines the ratio Zo1/Zll. The (e,e') reaction is well understood, and yields a second independent equation for Z01 and Z l l , as seen in table 1. The measured (e, e') cross sections, therefore, determine the magnitude of the Z-coefficients. The results of this analysis are shown in table 2. The errors encompass the range of solutions allowed by the quadratic term in eq. (2) and the measured limits on the pion crosssection ratios. We find that the observed transitions to the T = 1 states exhaust 33 to 45% of the total isovector transition strength, but only 1 to 15% o f the isoscalar transition strength. As suggested by the calculations o f Millener [8] and by preliminary (n, Tr') results, other 4 - , T = 1 states reached by strong isoscalar but weak isovector transitions may be present in this excitation region, but would not be seen in (e,e') because magnetic electron scattering is most sensitive to isovector transitions. Neglected effects such as Coulomb and nuclear distortion, Fermi averaging, and the contributions of nonresonant 7rN partial waves have been estimated, using standard computer codes [ 14], to modify the deduced Z01 coefficients by less than 6% and the Z l l coefficients by less than 1%. The ratio of the 7r- cross section for the 11.7 MeV state to the n + cross section for the 17.3 MeV state can be used to further restrict the allowed values of the Z-coefficients, but this procedure depends more strongly upon the model-dependent distorted-wave analysis. With the Z01 and Z l l so determined, and using Z12 = 0.40 + 0.04 extracted directly from the electron scattering cross section for the purely isovector transition to the T = 2 state, it is possible to evaluate from eq. (1) the cross-section ratio o2/01. The results for the relative 7r+ and 7r- cross sections for the T = 2, 18

j~r = 4 - , 24.3 MeV state are shown in table 2. The n - (rr+) cross section for the 24.3 MeV excitation is predicted to be between 0.15 and 0.77 (0.21 and 0.88) times that of the T = 1, 11.7 (17.3) MeV excitation. Thus, even though the T = 2, 24.3 MeV state is strongly excited in the (e, e') measurements, it has not been clearly observed in pion scattering due to the lower sensitivity to isovector transitions. In summary, (e, e') cross sections, measured for strongly excited T = 1 and T = 2 states in 14C, have been combined with existing (zr, lr') cross-section ratios to determine the isoscalar and isovector spin transition amplitudes. With an assumed effective interaction, and subject to the limitations previously discussed, the extracted values of Z01, Z l l , and Z12 can be used to predict absolute (n,n'), ( p , p ' ) and (p,n) cross sections. Comparison of such predictions with experiment may test the strengths of the contributing isoscalar and isovector terms in these reactions. These results are expected to be less uncertain than those using Z-coefficients obtained from nuclear structure calculations. The serious question that remains, however, is that large-basis shell model calculations predict cross sections that are too large by at least a factor of 2 to 3. Thus an additional mechanism, be it further fragmentation or true quenching of the transition operator, must be invoked to explain these results. We thank John Millener for communicating the results of his calculations.

References [1] [2] [3] [4] [5]

T. deForest and J.D. Walecka, Adv. Phys. 15 (1966) 1. R.A. Lindgren et al., Phys. Rev. Lett. 42 (1979) 1524. J.A. Carr et al., Phys. Rev. C27 (1983) 1636. R.S. Hicks et al., Phys. Rev. C21 (1980) 2177. J.B. Flanz, Ph.D. Thesis, University of Massachusetts, unpublished (1979).

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PHYSICS LETTERS

[6] L.A. SchaUer et al., Nucl. Phys. A379 (1982) 523. [7] D.B. Holtkamp et al., Phys. Rev. Lett. 47 (1981) 216. [8] D.J. MiUener and D. Kurath, Nucl. Phys. A255 (1975) 315; D.J. Millener, private communication. [9] G.C. Ball et al., Phys. Rev. Lett. 31 (1973) 395. [10l H.W. Baer et al., Los Alamos National Laboratory Report LA-UR-83-366, to be published. [11] J. Dubach, Nucl. Phys. A340 (1980) 271.

22 March 1984

[12] J. Raynal, Nud. Phys. A97 (1967) 572. [13] F. Petrovich and W.G. Love, Nucl. Phys. A354 (1981) 499. [14] J.A. Carr, F. Petrovich, D. Halderson and J. Kelly, scattering potential code ALLWRLD, unpublished; J.A. Carr, distorted wave code MSUDWPI, unpublished, adapted from the code DWPI, R.A. Eisenstein and G.A. Miller, Comput. Phys. Commun. 11 (1976) 95.

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