Nuclear Physics A309 (1978) 115- 127; ( ~ North-Holland Publishino Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

THE ZH(~, p~)n REACTION AT 7.5-7.9 MeV c.m. ENERGIES

HIROSHI NAKAMURA

College of Science and Engineering, Aoyama Gakuin University, Tokyo

and

HIROSHI NOYA

Department of Physics, Hosei University, Tokyo

Received 30 January 1978

(Revised 2 June 1978)

Abstract: The 2H(ct, pct)n reaction at 7.5-7.9 MeV c.m. energies has been analyzed by the use of the modified impulse approximation. All the experimental data have been reproduced reasonably well by the same approach as for the 10 MeV case and the destructive interference of the n-p final state interaction has again been clearly observed as in the 6 MeV case. Some inferences for reaction mechanism are presented.

1. Introduction

In a previous article 1), we studied the vector analyzing powers and differential cross sections in the 4He(d, p)n4He reaction at 10 MeV c.m. energy by the use of the modified impulse approximation (MIA) 1-3) based on the ~-n-p three-body model. It was found that a reasonably good fit to the data is obtained by the MIA, if the difference 4) between 5He-p (SLi-n) and ~-p (s-n) phase shifts is taken into account adequately. The magnitudes of the optimum q~ were considerably large for S-, P- and D-waves.

However, in the former MIA analyses 4.5) of the differential cross sections in the 2H(~, p~)n reaction at 5-6 MeV c.m. energies, we adopted a somewhat different approach. Namely, in order to reproduce the data, several new terms were introduced in the reducing factor 1-3) while the phase difference ~b was not taken into account. Considering that the major term, the Cr term, has a characteristic parity dependence, we suggested 4, 5) at that time that this term arises from a three-nucleon transfer reaction, which is not included in the ~-n-p three-body model.

In this article, we attempt to understand the C r term within the framework of the ct-n-p three-body model and conclude that there is no essential difference between the above two approaches.

Recently, data from the 2H(~, p~)n reaction at 7.5 MeV [ref. 6)] and 7.9 MeV [ref. 7)] c.m. energies have been reported. In this article, we analyze these data by

115

II6 H. NAKAMURA AND H. NOYA

the use of the MIA and utilize the results for the above purpose. We also investigate

the effects of the n-p final state interaction (n-p FSI) from these data by the same

method as in refs. 4.5.8).

2. Analysis

In the MIA analysis, the initial state interactions in the r-d channel and the final

state interaction in the ‘He-p (5Li-n) channel are introduced through the reducing

factor r(Y) [= c(Y)/C(Y)], h w ere c(Y) represents the partial amplitude for state Y

involving initial and final state interactions, while C(Y) is that of the impulse approx-

imation.

In this article, we analyze the data of 7.557.9 MeV cm. energies adopting the

reducing factor which we used in the analyses of the vector analyzing powers and

differential cross sections at 10 MeV c.m. energy ‘), as well as the neutron polariza-

tions and differential cross sections at 33 MeV c.m. energy 9). Here we summarize

the method of ref. ‘).

The reducing factor for the ‘He-p exit channel is given by

r(Y) = +x(L,)[i;,+i,][l +R,(&: h)].

(2.1)

where the quantities with a bar and subscript p Lepresent the quantities in the 5He-p

system, whereas those with a subscript d are for the cc-d system. The superscript R

means the real part, and L and J are respectively the orbital and total angular

momenta. The notations q(LJ), 6(LJ) and a(L) represent the absorption coefficient,

phase shift and the Coulomb phase shift, respectively. The real parameter SI(&),

the reduction parameter, represents the reduction of the partial amplitude due to

the initial state interaction. The term R,(Ld : h) represents the h-dependence of the

reducing factor which arises from the n-p FSI and 6Li -esonances as well as the

prominent reduction of the partial amplitude around the (t)- ‘He level, where h

represents the rx-n relative momentum in ‘He. The reducing factor for the 5Li-n

exit channel is given in the same way.

Since ‘He-p phase-shift data are not available, the following expression is assumed:

2qLJ) = cs,(LJ)t- 4(L) [S”(LJ) = h”(L.4 + 4(L)], (2.2)

where the quantity with subscript p but without the bar refers to the u-p system,

and 4(L) represents a real adjustable parameter. The quantities with subscript n

refer to the ‘Li-n or a-n system. We put f;, = L, = L, J, = J, = J, neglecting the

spin of 5He (5Li).

In the present analysis, the phase difference 4(L) is taken to be 0 for L 2 3. As

for the R, term, we use the same form as the first solution given in the latter half of

ref. 5), i.e.,

2H(~, p~)n 117

Rt(La:h) = 0, for L a ~ 2,

~ - 4 ( h z - h ' ) ( h - h l ) / ( h 2 - h l ) 2, for h I -< h _< h 2

Rt(2" h) = [0, for other cases, (2.3)

h 2 = 2h(2) -h l ,

where h(La) represents the possible zero point of the reducing factor and h 1 (= 0.20 fm -1) is the value o fh at the (3) - 5He level. If the same R, term as in ref. 1) is used, the results become somewhat worse but there is no essential difference. The reduction parameter e(Ld) is taken to be unity for L a > 3 and 0 for L d = 0 as in ref. 1).

Using six free parameters ct(1), ~(2), q~(0), ~b(1), q5(2) and h(2), we search for the best fit to the data of 7.5 MeV c.m. energy 6). The optimum values are tabulated in table 1, and the results are illustrated in figs. 1 8.

TAI~Lr 1

The M I A parameters in the range E~.m. = 5 10 MeV

E~ ..... (MeV) 5 6, 7.5 7.9 l0 ~)

a(1) 0.20 0.20 0.20 c~(2) 0.30 0.25 0.40 ~b(0) (deg) - 30 - 15i 0 30 qS( 1 ) (deg) 40 30 55 q5(2) (deg) - 20 - 20 - 20 h(2) ( fm-1) 0.4 0.4 0.4

~) Ref. 1).

The shift of the second 5He peak toward small arclength (s) is well reproduced. This shift is mainly due to the interference between the processes for the 5He-p and 5Li-n exit channels. Also, various partial waves in the 5He-p exit channel take part in this shift. To illustrate this situation, we take one typical example, (0p, 05, ~b,) = (69.0 °, 15.2 °, 180% and introduce a ratio

7 = ]Smaxl2/lSres] 2, (2.4)

where Smax and Sre ~ represent respectively the scalar amplitudes (S) at s = 7.4 and 7.8 MeV, whose definition is given in ref. s). The former corresponds to the maximum of the experimental energy-correlation spectrum of the cross section, while the latter corresponds to the (~)- 5He resonance. Since the magnitude of the differential cross sections in these geometries is approximately proportional to IS[ 2, it is possible to estimate the value of 7 from the experimental cross sections. The empirical value of 7 thus estimated is ~ 1.3 indicating clearly the shift of the 5He peak. If a theory fails to reproduce the shift of the 5He peak, the value of 7 in that theory is, of course, smaller than unity.

118 H. N A K A M U R A A N D H. N O Y A

x

E

E

" o

- 1 3

10 I . . . . . . . . . , . . . . . . . . . a

ca= ,;,.0" 5 % ' : 1 8 0 . ¢

0 . . . . . . . . . . . . . . . . . . j

5 10

lO

,r,, % = 79~0

I1~ ~ o.= ,28' J " l .I, '~;':'8°°'

0 • . . . . . . . . . , . . . . . . . . . r

o 5 1o

1 0 , , , , , , , , . i , , , , . . - - ,

5 e & 8.4 ° ' I ¢~o( 18o.o" l ! s '

5 . ! I "

o 5 lO

I0

0 0

5 ~ 9"5° 1522 °

5 10 S ( M e V )

Fig. I. Experimental 6) and theoretical differential cross sections for the reaction =H(~, pct)n at 7.5 MeV c.m. energy, ~p = 0, and other angles as indicated. As was clone in ref. 0) interfering processes are denoted as (1) n-p FSI, (2) ~t-p OFS, (3) zt-p FSI, (4) p-15N* coincidences and (5) ct-n FS[ at E,, = 0.96 MeV. The theoretical values (dashed curves) are calculated by (2.1)-(2.3). The solid curve represents the corrected values by the inclusion of the n-p FSI with (2.6) (2.8) and E o = 1.5 MeV, r = 0.6 and

= 0. The dashed curve is identical with solid curve for Enp > E o.

~o

x

d

"o

1 0 ' . . . . . . . . . i . . . . . . . . . i . . . ,

5 Bet = 5.5° , I ~:,8oo" "% I t v I .~ . | f ! (

%,oZ,4, " \ J I l L " l l ' ~ ~ | -

o . . . . . . . . . , . . . . . . . . . , - J | o 5 lO

1(~1 . . . . . . . . . i . . . . . . . . . h . . . . .

5 e~: ~o.d' I ~ . = 180"0°

5, I|gl m / ~ '

% , 0 . . . . . . . . . u . . . . . . . . . , . . . .

5 10

Op = 71.7 °

1 0 , .~ . . . . . . . . . i . . . . . . . . . t . . . . . 5 ,,

,~ I 8 o = 1 4 5 " ' ~ I ¢ a = 1 8 0 . 0 °

,,F.. 0 . . . . . . . . . •

0 5 10

1 0 ] . . . . . . . . . i . . . . . . . . . 1 . , , , ,

5 8a= 11"0~ j .5 ~ a = 1 5 5 . 7 °

l . ]

• | F ?.- • a m •

. . . . . . . . . , . . . . . . . . . J . . . .

5 10 S ( M e V )

Fig. 2. See caption to fig. 1.

~o ×

%

( 9

E

2H(.=, p e o n

1 0 I . . . . . . . , . , . . . . . . . . . J . . . . .

5 8e: 5.9" ¢~=180.0 °

0 . . . . . . . . . i . . . . . . . . . I . . . . .

o 5 lO

~0

-o

op= 6~o' 1 0 ' . . . . . . . . . i . . . . . . . . . = . . . . .

^5 9(X= 1 5 . ~ , , ~ . ~=180.0

0 . . . . . . . . . i . . . . . . . . . i . . . . 0

0 5 10

, , , I . . . . . [ . . . . . . . . i . . . . .

ea= 10.6 ° ! 5 ~a:lBO.O °

5 10

l O j . . . . . . . . . i . . . . . . . . . J , , , , ,

Oo,= 11.6 ° 5 5 q~a= 15&O°

o 5 lO S CMeV)

F i g . 3. See c a p t i o n to f ig. l .

119

~O

x

d "

E e ~

E

d

t / )

0 0

. . . . . . . . . J . . . . . . . . . , . . . , , , , ,

ea = 6.6 ° , 5 $o :~8o.o"

. . . . I . r . I . . . . . . . . . , . . . . . . . |

5 10

10

0p=62.5 "j . . . . . . . . . , . . . . . . . . . I . . . . . . . .

I~ e,-.,= 16.0" ! /I / t l I I

5 10

. . . . . . . . . I , , . . . . . . , i . . . . . . . .

Oa= 11.8 °

5

g lO

I0~ . . . . . . . . . = . . . . . . . . . ~ , , , , , , , Ca= 127 ~ $c~:158.3 °

i n

0 ! . . . . . . . . . , . . . . . . . . . , . . . . . . . . o 5 lO

S ( M e V )

F i g . 4. S e e c a p t i o n t o f ig. 1.

120 H . N A K A M U R A A N D H . N O Y A

~o ),( 5

c~ L ul

> @

E

J21 Y

G)

"o

1 0 ' . . . . . . . . . i . . . . . . . . . i . . . . . . . . i , Oct: 7.9 °

5 ~a=180 .0 °

"' I

0 . . . . . . . . . i . . . . . . . . . i . . . . . . . . . i , 5 10 15

10 i . . . . . . . . . i . . . . . . . . . , . . . . . . . . . i , e o : 12.4 ° @~=180.0 °

5

i | l

0 . . . . . . . . . , . . . . . . . . . ! . . . . . . . . . i , 0 5 10 15

~ 0

x

E J~3 E

"o v3

Op = 59.3 °

1 5 ' . . . . . . . . . i . . . . . . . . . J . . . . . . . , , .L,,_ 5 O~= 16.9'

I I ~a=180"0° I

5 1

/ e l I i l l e l I i

5 I0 15

10 ' . . . . . . . . t . . . . . . . . . , . . . . . . Oct = 13 200

5 5 ~c :159 9

i l I i

5. , l i • • II I ,

I • i n

5 10 15

S ( M e V )

F i g . 5. S e e c a p t i o n t o f ig . I .

Op= 55 .5 '

10 ' . . . . . . . . . i . . . . . . . . . i . . . . . . . . . i . . . . . e~= &:t '

/ ' , , { a = 180.0 °

5

o 0 5 10 15

10 L . . . . . . . . . i . . . . . . . . . i . . . . . . . . . * . . . . . e ~ = 13.0 ° ~ = 1 8 0 . 0 °

5

I 5 I

5 1 2 I ,

0 . . . . . . . . j . . . . . . . . . ! . . . . . . . . . i . . . . 0 5 10 15

i . . . . . . . . i . . . . . . . . . i . . . 15 . . . . . . . . . " 5 0¢~ = 1 7 , ~

¢ ~ : 180 .0

i ~0-4

5 1 1 ] = ~ l

o . . . .

0 5 10 15

0 ! . . . . . , , , , i , , , . . . . . . i . . . . . 4 ec~= 13~'

0 c ~ : 1 6 0 0 ° 5

~-I 1 %

t,~,, ' " ' %,

O / . . . . . . . . . , . . . . . . . . . , . . . . . . . . . , . . . .

5 10 15

S ( M e V

F i g . 6. S e e c a p t i o n t o f ig . 1.

The MIA scalar amplitude is given by a sum,

S = S v + S .,

S p = ~ S p ( L d ) , S n =

L d = O

• S.(Ld), L d - - 0

(2.5)

2 H ( ~ , p~z)n 121

-o

%

E

E

d CL.

" 1 3

U 3 " 1 3 &" ' 1 3

10

. I L ~ . . v . . . . . . . . i . . . . . . . . . i . . . . . . . . . l . . . . . . . .

l,,tt\ ~,,-~<

l~ i i 3 " ~ " t~ ,~,= 1800 . . . . . . . . r r . . . . . . . . . i . . . . . . . ' ' l . . . . . . . . . t . . . . . . . .

5 10 15 20

10 .................... ' ......... ' ............... '2' Ocx= 12.0 %~=180.0 °

0 . . . . . . . . . t . . . . . . . . . i . . . . . . . . . i . . . . . . . . . t . . . . . . . .

0 5 10 15 20

ep=4o.o'

1 o i . . . . . . . . . i . . . . . . . . . , . . . . . . . . . i . . . . . . . . . i ........ - •

s s I

0 . . . . . . . . . I . . . . . . . . . i . . . . . . . . . i . . . . . . . . . ~ . . . . . . .

5 10 15 20

I 0 1 . ~ . . . . . . . . . 1 . . . . . . . . . I . . . . . . . . . I . . . . . . . . . 1 . . . . . . . . o I

Oe= 13.2 J ~ct=154.7 °

5

0 5 10 15 20

S ( M e V )

F i g . 7. See caption t o f ig, 1.

h . . . . . . . . . i . . . . . . . . . i . . . . . . . . . I . . . . . . . . . i . . . . . . . . . I , ,

is e0.= 7 8 °

2 3 E , t , .

N I I i

0 5 10 15 20 25

~ 10

U ' )

8p = 33.1'

1 0 l . . . . . . . . . t . . . . . . . . . i . . . . . . . . . i . . . . . . . . . i . . . . . . . . . h .

• 8 0 . = 1 9 . 0 °

: ~a=180.0~

5" 5 5 4 3 I , . . . . . . J . . . . . . . . . i . . . . . . . . . i . . . . . . . . . i . . . . . . . . i "

0 5 10 15 20 25

. . . . . . . i . . . . . . . . . i . . . . . . . . . i . . . . . . . . . I . . . . . . . . . I . ,

/ " N 80.= 13.0 ° / ~ . ~ 0o~ =18 0.0 ° -

. . . . . . . . . i . . . . . . . . . i . . . . . . . . . J . . . . . . . . . t . . . . . . . . . w ,

5 10 15 20 25

1 0 j . . . . . . . . . t . . . . . . . . . I . . . . . . . . . i . . . . . . . . . I . . . . . . . . . I , ,

0 ~ : 1 4 1 °

; ¢~ =156.4 ~ 4 4

5

,4 i ;

0 I . . . . . . :.., . . . . . . . . . , . . . . . . . . . , _ . - z . ' . . ,~= . . . . , . . 0 5 10 15 20 25

$ CMeV)

F i g . 8. See caption t o f ig. 1.

where Sp(Ld) [S,(Ld) ] represents the scalar amplitude for the 5He-p (SLi-n) exit channel and the ~-d entrance channel with orbital angular momentum L a. We tabulate in table 2 the values of these scalar amplitudes at s = 7.4 and 7.8 MeV. The MIA y calculated by formula (2.4) and the S given in (2.5) is 1.4, being quite consistent with

122 H. N A K A M U R A A N D H. N O Y A

TABLE 2

The scalar ampli tude in fm ~ 2 for each partial wave at (0p, 0~. 4)~) = ( 69.0°, 15.2 °, 180 °)

Exit channel

5He-p

5Li-n

s - 7.4 MeV s = 7.8 MeV

Sp(O) 0 0 Sp(l) 27.3 12.8i 31.1 + 3.7i Sp(2) 2.1.3-11.8i 25.7+ 2.1i Sp(3) - 1 . 5 + 6.5i - 5 . 1 + 1 4 . 2 i So(4 ) 21.8 - 42,0i 2.3 - 44.4i So(5) - 7 . 5 - 2 2 . 9 i 5.7 26.1i Sp 23.5 79.2i 6 2 . 7 - 46.7i

S. - 7.5 - 13.4i 9.9 - 1Y2i

S 16 .0-92 .7 i 52.9 60.0i

the empirical value 1.3. However, if the scalar amplitude Sn is not included in the calculation, the value of 7 decreases to 1.1. If a sum Sp(0) + Sp(1 ) + Sp(2) is used instead of S, 7 drops further to 0.9 and the shift of the 5He peak does not occur.

A clear discrepancy around E,~ = 0 which may come from the n-p FSI is observed

for (0p, 0~, qS~) = (62.5 °, 16.0 °, 180°), where Enp represents the n-p relative energy. In the present article, we at tempt to extract the n-p FSI in this geometry using the same method as in ref. 8). Note that we analyzed the n-p FSI in ref. 8) under almost the same kinematical conditions as in the present analysis. The scalar amplitude S t"m induced by the n-p FSI can be written as

s(npJ(x, Enp ) = c[P3(x)/P3(xo) ][t(Enp/Eo)/t(ff~p/Eo)], (2.6)

with

~ 1 - 3 ,2, for lYl ~ 1

t (y) = (0, for [Yl > 1,

x = f¢" I¢', k ' = n + p ,

(2.7)

c = - Co(1 - rei~). (2.8)

where n and p represent respectively the c.m. momenta of the neutron and proton in the final state, k the c~-d relative momentum in the initial state, PL(x) the Legendre polynomial, c a complex parameter, E 0 the range of E,p where the n-p FSI is effective, and x o is the value of x for the minimum value Enp of Enp allowed by the geometry. It i s a s sumed that the n-p FSI occurs only in the F-state of the c~-d channel. For the above geometry, the values of Enp and x 0 are 0.15 MeV and 0.53, respectively, and the MIA scalar amplitude at Enp = E,p is -54 .3 + 40.3 i fm ~ ( = Co). The param- eter c can be written as

:H(~, p~)n 123

A g o o d agreement with data is obtained at

E o = 1.5 MeV, r = 0.6+0.1, I~1 < 60°- (2.9)

The results for r = 0.6, ¢ = 0 are illustrated in figs. 1 8. The destructive interference of the n-p FSI is well observed. I fE o is taken to be 0.6 MeV as in ref. 8), the agreement with the data becomes worse.

Using the same parameters, we also calculate the differential cross sections for 7.9 MeV c.m. energy. The results are illustrated in figs. 9 and 10. The agreement with the data at quasi-free peak is fairly good (fig. 9) though the theory somewhat over- predicts for small 0p. The results for small E.p also fit the data fairly well (fig. 10) but,

J

_ , , o o

_ , , o o

.oo / j , , \ \

400J ,fOfOfOfOfOfOfOf~~, t i i i ,

5 10

ep = 40"

i

5 1C ep : ~¢

= o

II l I l I I I I I

5 10

Op= 45 °

600

2OO

i I

5 10 ep ~ 55"

1

1 1 i

5 10 5

% [M~vj

I J

600

200

I

lo

Fig. 9. Experimental 7) and theoretical differential cross sections for 2H(~, pct)n at 7.9 MeV c.m. energy, plotted against the energy of the emitted proton Ev(MeV ). In these spectra, 100 counts per channel corresponds to 19.6 mb/sr 2 [ref. 7)]. The theoretical values (solid curves) are calculated by (2.1)-(2.3) involving the same n-p FSI as in figs. 1 8. The change of the theoretical values-due-to the inclusion of the

n-p FSI is negligibly small in these ge, onl~tries.

124 H. N A K A M U R A AND H. NOYA

9 -'/t 8

I 7 % 6

Q . I..IJ '~ 5 O4 "13

~4 4-

3

2

-//

I I I I /

t' ~ " ' ~ " ¢)J

0p=47 °

O~ = 20*

I 1 I 1 2 3 4 5

Ep(MeV) Fig. 10. Same as fig. 9, butdifferential cross sections are given in mb,'sr 2 • MeV. The theoretical values (dashed curve) are calculated by (2.1)- (2.3) as in figs. I 8. The corrected values by the inclusion of the n-p

FSI are given by the solid curve (E, = 1.5 MeV) and by the dot-dash curve (E 0 = 0.6 MeV).

in contrast to the results for 7.5 MeV c.m. energy, the best fit to data is obtained at E o = 0.6 MeV.

3. Discussion

A reasonably good fit to the data from the 2H(~, pe)n reaction at 7.5 7.9 MeV c.m. energies has been obtained by the use of the same method as at 10 MeV c.m. energy 1). It should be, emphasized that the shift of the second 5He peak toward small arclength in the data of 7.5 MeV c.m. energy has been well reproduced. The destructive inter- ference of the n-p FSI has been observed again.

In the previous works 4, 5), in order to reproduce the data at 5 6 MeV c.m. energies, we introduced a C r term in the reducing factor and presumed that it arises from a three-nucleon transfer reaction. However, one should note that the major part of the C r term can be absorbed in the phase difference q~(L). In fact, the data of 5-6 MeV c.m. energies 4.2) can be fitted fairly well by the present approach, if one assume that

phase-difference 4~(0) has an imaginary part. We tabulate in table 1 the opt imum values of the parameters for the c.m. energy E . . . . in the range between 5 and 10 MeV. Note that, at E .. . . = 5-6 MeV, qSR(L) depends on the parity by a factor ( - 1) L+1 as does the C r term 4, s). It is f rom this characteristic parity dependence that we presumed the C r term to have arisen from a three-nucleon transfer reaction. The energy varia- tion of phase difference 4)(0) has further striking features, i.e., (i) the sign of ~bR(0) changes from positive to negative as E . . . . decreases from 10 to 5 MeV and (ii) ~b~(0)

2H(~, p~)n 125

is negative. Here the superscript I represents the imaginary part. In the following, we show that the above characteristics of qS(L) can be understood within the framework of the ~-n-p three-body model. The channel in which the n-p subsystem is in the scattering state (n-p scattering state channel: n-p SSC) plays a very important role in our discussion.

Before entering on this problem, we discuss briefly the n-p FSI, which is the final state interaction in the n-p SSC. The contributions from the n-p FSI in the 3S 1 state to the matrix element ( [ T I ) can be written as

- ( [PsTI ) + (qJ~-)[PsTI), (3.1)

where T represents the ~-n-p three-body T-matrix of the breakup reaction in which the n-p FSI is eliminated, Ps the projection operator to the as 1 n-p state, I ) the plane wave in the initial or final state and ~u~-) the n-p scattered wave function with n-p relative momentum q obeying the incoming-wave boundary conditions. The second term of (3.1) may not be important because, in deuteron-nucleus reactions, the major part of the incoming deuterons in general return to the deuteron channel. Evidently, the first term interferes destructively with the matrix element ( I T I ). This is the reason why the n-p FSI interferes destructively with the other processes. The first term of (3.1) can be divided into an almost En, independent part and a sensitively E,p dependent part. The major part of the former is absorbed in the reduction parameters and Rt terms and only the latter, which vanishes outside a narrow region around E,p = 0, remains. Therefore, the n-p FSI which we have deduced in the present analysis and in ref. 8) is very likely ta be the sensitively E.p dependent part.

Let us discuss the contributions from the n-p SSC in the intermediate state. Since the SHe-p and 5Li-n channels are symmetrical in the present discussion, we take here- after the 5He-p system only. We consider that the ~-n subsystem is in a quasi-bound state corresponding to the 0 SHe level. In the MIA, the contributions from the n-p SSC are involved in the final state interaction in the SHe-p channel. If the e-p interaction is sufficiently strong in the 5He-p system, the n-p interaction is embedded in the c~-p interaction and both of the interactions are incorporated as a SHe-p inter- action. Since the 3S 1 n-p force is attractive, the sign of the phase difference ~b produced by the n-p interaction is positive. In fact, for 1he P-wave 5He-p system, 4) takes a considerably large positive value [q~(1) = 30-60°]. Note that the c~-p subsystem has the same orbital angular momentum as the SHe-p system in the first approximation and, therefore, a strong c~-p interaction occurs in this case.

However, if the e-p interaction is weak, the proton interacts impulsively with the neutron in SHe, because the range of the n-p interaction is estimated to be considerably smaller than the radius of 5He. Then, in the first approximation, the matrix element of the SHe-p scattering may be factorized into a term describing the ~-n relative motion in 5He and a matrix element ( ITnpl ) for the n-p system, where T,p is the n-p two-body T-matrix which automatically includes multiple scattering effects between neutron and proton. Since the n-p phase shift for the 3S1 state is negative by virtue

126 H. N A K A M U R A AND H. NOYA

of the deuteron pole in Tnp, it is inferred that the effective n-p force in SHe-p scattering is repulsive. Namely, the phase difference 4) may be negative for a weak ~-p interaction. This may be the reason why ~b takes a negative value for the D-wave SHe-p system [th(2) = -20° ] , in which the ~-p interaction is negligible.

As for the S-wave 5He-p system, the behavior of ~b as a function of E .. . . is not simple. The S-wave phase shift 6p(~) for the average kinetic energy of the ~-p sub- system varies from - 6 0 ° to - 2 5 ° as E .. . . decreases from 10 to 5 MeV. This indicates that the effective ~-p interaction, which is considerably strong at E .. . . = 10 MeV, weakens rapidly as Ec.m. decreases and, consequently, the sign of ~b may change from positive to negative. In fact, ~bR(0) has such a behaviour as a function of E .. . . and.

at E . . . . = 5-6 MeV, q~R(L) begins to have apparently a strong parity dependence. The n-p two-body T-matrix has a property similar to the ~-p two-body T-matrix

in that both of them have a single pole corresponding to the deuteron state and.the spurious (1)+ 5He level, respectively. This indicates that, by the incorporation of the n-p and c~-p two-bodyT-mat r ices in the 5He-p channel, an enhancement of reaction strength occurs. Since the contributions from the n-p SSC increase rapidly as E .. . . decreases, this mechanism may become important for small E .. . . . This may be the reason why q~(0) has a negative imaginary part at E .. . . = 5-6 MeV, representing the enhancement of reaction strength.

Recently, an analysis of the ~-d breakup reaction by the use of the Faddeev equation based on the c~-n-p three-body model has been reported by Koike l o). According to his analysis, no three-nucleon transfer reaction was found. From this, it is inferred that the above understanding of the reaction mechanism is correct. Also, his analysis seems to support our prediction for the n-p FSI in refs. 3. s) because he found that the n-p FSI interferes destructively with the other processes as we predicted. Furthermore, he found that a strong n-p FSI, effective in a wide region of E,p, occurs in the S-, P- and D-waves of the c~-d channel as well as in the F-wave. This may support our conjecture for the n-p FSI presented in this article, i.e., the sensitively E,p dependent part of the n-p FS! was observed in the present work and in ref. 8).

As a conclusion, we think that the expressions (2.1) and (2.2) for the reducing factor may be adequate for the partial waves, except for D~, 2 waves, being consistent with the analysis by the Faddeev equation. We would like to remark that the empirical reducing factor obtained in the present analysis includes the E,,p independent part of the n-p FSI. As for D~, 2 waves, the contributions from the 6El levels must be taken into account in a more adequate way.

The authors would like to acknowledge the cooperation of Mr. M. Kadoi and the computer staff of Hosei University where the numerical calculations have been performed. We are very thankful to Dr. Y. Koike for stimulating discussions and for providing a part of his results in advance of publication. Finally, we express our sincere thanks to Dr. K. Prescher for providing the details of his data.

2H(~, p~)n 127

References

1) H. Nakamura, H. Noya, S. E. Darden and S. Sen, Nucl. Phys., in press 2) H. Nakamura, Nucl. Phys. A208 (1973) 207 3) H. Nakamura, Nucl. Phys. A223 (1974) 599 4) I. Koersner, L. Glantz, J. Johansson, B. Sundqvist, H. Nakamura and H. Noya, Nucl. Phys. A286

(1977) 431 5) K. Sagara, T. Motobayashi, N. Takahashi, Y. Hashimoto, M. Hara, Y. Nogami, H. Nakamura and

H. Noya, Nucl. Phys. A299 (1978) 77 6]. K. Prescher, W.Bretfeld, W. Burgmer, H. Eichner, H. J. Helten, H. Klein, H. Kretzer, H. Stehle and

W. W. Wohlfarth, Nucl. Phys. A286 (1977) 142 7) T. Rausch, H. Zell, D. Wallenwein and W. von Witsch, Nucl. Phys. A222 (1974) 429 8) K. Sagara, T. Motobayashi, N. Takahashi, Y. Hashimoto, M. Hara, Y. Nogami, H. Noya and

H. Nakamura, Nucl. Phys. A273 (1976)493 9) P. Lelex, M. Bosman, P. Lipnik, P. Macq, J. P. Meulders, P. Petit, C. Pirart, G. Valenduc, H.

Nakamura and H. Noya, Phys. Lett. 70B (1977) 163 10) Y. Koike, Proc. Int. Conf. on nuclear structure, Tokyo (1977) p. 41 ; Nucl. Phys. A301 (1978) 411