The photodisintegration of the deuteron

-~

Nuclear Physics 32 (1962) 637--651; ~ ) North-Holland Publishing Co., Amsterdam Not to

be reproduced by photoprint or microfilm without written permission from the publisher

THE PHOTODISINTEGRATION

OF T H E D E U T E R O N

A. DONNACHIE ¢ The

University, Glasgow

Received 9 December 1961 Differential cross-sections and polarizations are calculated for photon laboratory energies up to 130 MeV. The calculations are carried out both for a 4 % and a 6 % deuteron D-state probability, the final state being described by the Gammel-Thaler type Y.L.A.M. phase parameters obtained in the recent analysis of Breit et al. Electric dipole and quadrupole triplet transitions and magnetic dipole and quadrupole singlet transitions are considered, and the coupling taken into account. The results obtained are compared with experiment, and compared and contrasted with those of previous calculations using Signell-Marshak phase parameters.

Abstract:

1. I n t r o d u c t i o n

In principle, the investigation of the photodisintegration of the deuteron can give information either on the radiative interaction, if the initial and final state wave-functions are known, or, on the other hand, if the radiative interaction is known, on the neutron-proton interaction. It is generally with the latter point in mind that deuteron photodisintegration is investigated, since the radiative interaction can be assumed to be well known, at least up to photon laboratory energies of 130 MeV. In this energy range, it has been shown that explicit inclusion of the mesonic field is unnecessary 1), and the interaction with the electromagnetic field m a y thus be taken as given on the basis of the gauge invariance of the non-relativistic Hamiltonian for the two-nucleon system. The photodisintegration proceeds mainly through electric and magnetic dipole transitions, the electric dipole transition being dominant. Electric and magnetic quadrupole transitions cause a marked interference in the angular distribution, but their contribution to the total cross-section is small. Higher multipoles m a y be ignored. On the basis of the above interaction several authors have calculated the angular distribution in the low and medium energy ranges. The total crosssection and angular distribution have been known for some time to show reasonably satisfactory agreement with theoretical calculation up to photon laboratory energies of about 10 MeV 2-5) on applying the Siegert theorem 6) for the electric dipole transitions. Until recently, however, theoretical work on the differential cross-section for photon laboratory energies between 20 and I50 MeV failed to account for the observed angular distribution, particularly t Present address: Department of Physics, University College, London. 637

~38

A. DONNACHIE

the large isotropic component 7-9). With purely central forces acting between the neutron and the proton, the electric dipole term is a pure sin20, and the magnetic dipole contribution to the isotropic component too small compared to the experimental value. It was not until a more sophisticated potential with tensor and spin-orbit forces was considered (which allows an electric dipole contribution to the isotropic term) that reasonable agreement with experiment was obtained. The calculation of de Swart and Marshak 10) showed clearly the importance of the deuteron D-state and the final 3F 2 state. Following on this, several papers were published 11-22) in which coupling 12, is, 17, 2o-22), higher radiation multipoles 14-17,2o-22) and retardation 12,19-21) were taken into account. Up to energies of 130 MeV it is generally accepted that retardation effects are of little importance 12, 21, 2~) but recently Matsumoto 19) has reported that they are essential at energies above 80 MeV. The angular distribution parameters appear to be sensitive to the percentage of deuteron D-state chosen. In the calculation of refs. 10,12,17) a D-state percentage of 6.7 is required to enable theory to fit the experimental data, although reasonably good agreement is obtained in refs. 11,14,21) employing a deuteron with a 4 ~o D-state. In the most recent calculations, in which good agreement with experiment is obtained up to photon energies of 150 MeV, Rustgi et al. 22) employ two forms of a modified Signell-Marshak potential, which give deuteron D-state percentages of 6.1 and 6.9. Polarization calculations are carried out in refs. 13,17,22). As yet there are no experimental data with which to compare the theoretical predictions. With the exception of Nicholson and Brown 12), and of Kramer is), the calculations have all been carried out using Signell-Marshak phase parameters. Nicholson and Brown use Gammel-Thaler phase-shifts for an electric dipole calculation at 130 MeV, and Kramer considers electric dipole transitions at four energies in order to compare different sets of phase-shifts, including Signell-Marshak and Gammel-Thaler phase-shifts. Both show that the GammelThaler solution is capable of reproducing the folded angular distribution, but no detailed analysis is made. In view of the recent phase-parameter analyses b y Breit et al. 23, 24) it is of interest to carry out a more detailed analysis of deuteron photodisintegration using their best solution, the so-called Y.L.A.M. set, which is a phase-parameter set of the Gammel-Thaler type, and to compare and contrast the results with the Signell-Marshak solutions. This is done for two different D-state percentages, namely 4 and 6. Phenomenological deuteron wave-functions are used, and wherever possible phenomenological two-nucleon continuum wave-functions are used in the final state. Otherwise they are calculated from the appropriate Gammel-Thaler potential.

PHOTODISINTEGRATION

2. The

OF

Multipole

THE

639

DEUTERON

Transitions

The deuteron wave-functions used are of the Hulth6n-Sugawara t y p e 25), i.e. VD(X) = V 4 ~

-Jr- %/-~

Z,,

(1)

where Ug(r) = cos 6g[l--e-a(~-~*)]e -~, Wg(r) = sin 6g[1--e-r(*-x*)] 2e-x I1 + 3(1--e-r*) + 3(1--e-rX)2]

z

~

(2)

J

a n d x ----- :or, Xc = o~re, with :t = 0.2316 fm -1, while the hard-core radius is t a k e n to be re = 0.4316 fm. For the two D-state probabilities chosen, we have N 2 = 7.6579 × 10 -12 cm -1, fl = 7.961,

7 = 3.798,

sin 6g = 0.02666 for 4 % D-state,

fl = 7.451,

7 = 4.799,

sin 6g = 0.02486 for 6 % D-state.

(3)

2.1. THE ELECTRIC DIPOLE TRANSITIONS The transitions 3S1+3D 1 --~ 3P0,

aP 1,

3P~+aF~

are the most i m p o r t a n t transitions for the photodisintegration at m e d i u m energies, a n d lead to an angular distribution in the c.m. system of the form ~--- a E l - ~ - b g l

The transition amplitudes

sin 2 0.

(4)

ELI appropriate to this case are

Eto = f~° o~rvlo(Pr ) [u,(r) -- V ~ w , ( , ) ] d , , Vn (~)r)[ug(r) + ½X/2Wg(r) Jdr,

ell = f7 El2 = cos

62 f 7 ar v]2(pr ) [ug(r)--l-~V-2w,(r)]dr

+ ~/{ sin E32

3

cos

(5)

62 ~ / 2 f 7 ~r v~z(pr)wg(r)dr, - - l" co

Jo

va2(~)Wg(r)dr

- - ~/~ sin ~2 f o :¢r vla2(pr)lUg(r)- 1-~%/2ug(r)]dr,

where the vLJ a are the final-state radial wave-functions, ~XLj tile phase-shifts and e2 the aPz--ZF 2 coupling parameter.

640

A. DONNACHIE

It has been shown lo) that a very good approximation to the triplet oddparity wave-functions is

pr [cos (5~LjiL(Pr)--sin ~LjnL(Pr)] for r_>-- R, VXLf(Pr) = pr cos ~SXLfiL(Pr) for re =< r < R,

(6)

where jL(X) and nL(X) are the spherical Bessel and Neumann functions. The range R is taken to be 1.4129 fm and the hard-core radius re to be 0.4316 fro. 2.2. T H E M A G N E T I C D I P O L E T R A N S I T I O N S The magnetic dipole spin-flip transitions 3S1+3D 1 ~ xS0,

1D 2

lead to the angular distribution M1 =

aMl+bM1 sinZ 0.

(7)

The appropriate transition amplitudes M f are

Mo = f o v°(pr)wg(r)dr'

M2 = f o v2(pr)wg(r)dr"

(8)

In this case, the potential acting in the final state is too strong for the radial wave-functions 5j(pr) to be approximated by eq. (6). Accordingly the wavefunctions are obtained by solving the Schr6dinger equation using the GammelThaler potential 26)

V(r) =

+oo

for

r
--Vo e-~* /zr

for

r ~ rc,

with V0 = 425.5, MeV,/z = 1.45 fm -1 and re = 0.4 fm. This potential gives a good fit to the 1S0 phase-shifts, of Breit fit to the 1D2 phase-shifts is rather poor. The magnetic dipole triplet transitions 3S1+3D 1 -+ 3S1+3D1,

(9)

et al., but the

8D2

have been shown 20) to give an entirely negligible contribution in the considered energy range, and are consequently neglected. 2.3. T H E E L E C T R I C Q U A D R U P O L E

TRANSITIONS

The electric quadrupole transitions zSI2I-ZD 1 - + 3S1-+-3D1,

3D2,

3D3+3G 3

are most important through their inteference with the electric dipole transitions,

PHOTODISINTEGRATION

OF THE DEUTERON

641

which causes a forward asymmetry in the angular distribution. However, t h e y also contribute to the term proportional to sin s 0, the complete contribution being given b y E2 = aE2-~-bE2 sins O+cE2cos O+dEscos 0 sin s 0+eE2 sin s 0 cos 2 0. (10) Since the electric quadrupole transitions are second order effects, the 3S 1 and 3D 1 final states are taken as uncoupled and the 3G3 state neglected. In this approximation the relevant transition amplitudes are

Eol = ½~/2 f ~

(O~Y)2 V01 (pY)Wg(~v)d ~',

E~l= fo

(ar) 2 v,x (pr ) [Ug(r)--½~/2wg(r) ]dr,

E22 = f :

(0¢r) 2 v22(Pr ) lug(r)+l%/2wg(r)]dr,

(::)

(~r) e v23 (pr)Iug(r)--1V2Wg(r)]dr. If the approximation (6) is a good one for the electric dipole amplitudes, it should be an even better one for the electric quadrupole amplitudes, and accordingly approximation (6) is made in evaluating eqs. (11). 2.4. THE MAGNETIC QUADRUPOLE TRANSITIONS We retain only the magnetic quadrupole singlet transitions 3S1-~-3D 1 --~ 1P1,

1F3,

which interfere with the magnetic dipole transitions, contributing to the parameters c and d, the effect on parameters a, b and e being negligible. The appropriate transition amplitudes, ?co

M , = jtJ c

o~rVl(Pr ) ~Ug(r)-- ~--~c/2wg(r) ]dr,

M3-- ~/-~ fo o~rv3(pr)wg(r)d,',

(12)

are evaluated using the approximation (6) for the radial wave-functions 731and ~3. This can be justified here b y the ,¢r term in the integrand. The magnetic quadrupole triplet transitions 3S1-~-3D1 ---> 3P1,

3P2-~-3F 2

are neglected. The results of the calculation of the above amplitudes are given in table 1, where for comparsion purposes we give also the corresponding Signell-Marshak results.

~42

A. DONNACHIE

TABLE

The transitio Ey

ElO En EI~ E32 Eol E~I E22 E2a Mo M~ Mx Ms

11.23 MeV

22.24 MeV

39.76 MeV

(1)

(2)

(3)

(1)

(2)

(3)

(1)

(2)

(3

0.876 1.261 1.123 0.474 --0.073 1.897 2.354 1.996 0.673 0.132 1.373 0.115

0.879 1.239 1.124 0.346 --0.062 1.912 2.368 2.013 0.671 0.141 1.389 0.111

0.993 1.482 1.297 0.185 0.050 1.97 2.42 2.08 0.813 0.159

0.416 0.803 0.574 0.439 --0.054 0.832 1.018 0.913 0.428 0.195 0.805 0.147

0.392 0.782 0.575 0.327 --0.046 0.843 1.024 0.917 0.426 0.209 0.813 0.144

0.411 0.863 0.644 0.215 --0.019 0.76 1.06 0.89 0.393 0.231

0.180 0.482 0.283 0.234 --0.022 0.335 0.428 0.362 0.242 0.219 0.462 0.149

0.412 0.498 0.278 0.269 --0.021 0.332 0.426 0.363 0.231 0.243 0.472 0.153

0.1 0.5 0.2 0.2 --0.0 0.3 0.4 0.4 0.2 0.2

(1) P r e s e n t calculation 4 % D-state. (2) P r e s e n t calculatio

As is to be expected, the general behaviour of both sets of amplitudes is similar. The most noticeable difference between the two is the very strong enhancement of Ea2 in the Gammel-Thaler solution at low energies. This is due to the large negative value of the coupling parameter e2 at these energies. Conversely, at higher energies the Gammel-Thaler coupling parameter becomes numerically smaller than the Signell-Marshak coupling parameter, with the consequence that Ea2 in the Gammel-Thaler solution becomes smaller than that of the Signell-Marshak solution. As we shall see, this has important repercussions on the angular distribution parameters. The other important difference is that M 2 in the Gammel-Thaler solution is smaller than M s in the TABLE

Differential cross, Ey

11.23 MeV (1)

aE aM a bE bM b

a/b fit /52

3.84 2.07 5.91 139.6 0.40 140 0.042 0.03 0.17

(2) 2.17 2.44 4.61 138.5 0.38 138.9 0.032 0.05 0.18

22.24 MeV (3) 2.71 1.51 4.22 135.2 0.51 135.7 0.031 0.05 0.20

(1) 5.34 0.28 5.62 57.2 0.56 57.8 0.098 0.06 0.24

(2) 4.19 0.36 4.51 53.3 0.61 53.9 0.095 0.07 0.24

39.76 MeV (3)

(1)

(2)

4.15 0.31 4.46 48.7 0.66 49.4 0.09 0.10 0.32

5.93 0.07 6.00 17.2 0.61 17.8 0.34 0.09 0.42

5.60 0.04 5.64 17.39 0.71 18.08 0.31 0.10 0.41

(3) 4.91 0.0~ 4.91 15.8 0.7, 16.5 0.3~ 0.1', 0.4'

o/ D-state. (2) ]?resent calculation 6 Tlle q u a n t i t i e s a and b are in/~b/sr. (1) P r e s e n t calculation 4/o

PHOTODISINTEGRATION

OF

THE

643

DEUTERON

a m p l i t u d e s in f m 52.3 MeV (1) 0.128 0.376 0.187 0.156 --0.012 0.213 0.236 0.257 0.172 0.224 0.366 0.136

77.3 MeV

(2)

(3)

0.079 0.391 0.174 0.212 --0.011 0.209 0.241 0.264 0.158 0.257 0.371 0.150

0.091 0.430 0.161 0.183 --0.030 0.21 0.28 0.31 0.139 0.282

(1) 0.096 0.269 0.108 0.100 --0.009 0.144 0.110 0.126 0.120 0.210 0.257 0.126

107.2 MeV

(2) 0.055 0.280 0.087 0.153 --0.007 0.122 0.128 0.129 0.104 0.254 0.251 0.138

127.3 MeV

(3)

(1)

(2)

(1)

(2)

0.045 0.318 0.067 0.158 --0.021 0.12 0.13 0.18 0.052 0.285

0.081 0.195 0.056 0.073 --0.002 0.115 0.067 0.084 0.098 0.172 0.193 0.105

0.053 0.209 0.040 0.104 --0.002 0.090 0.091 0.084 0.075 0.223 0.182 0.124

0.072 0.166 0.031 0.064 --0.001 0.109 0.058 0.077 0.091 0.158 0.172 0.096

0.052 0.179 0.022 0.089 --0.001 0.088 0.074 0.077 0.064 0.197 0.159 0.118

6 ~o D-state. (3) Signell-Marshak 6.7 ~) D-state (ref. 1~)).

Signell-Marshak solution, which again has an important bearing on the angular distribution parameters, in this case at the higher energies. 3. R e s u l t s The cross-section and polarization parameters obtained in this section are calculated using the formulae of de Swart 27). 3.1. THE ANGULAR DISTRIBUTION When we have unpolarized radiation, then, in the approximations made, we can write the angular distribution as

section p a r a m e t e r s 52.3 MeV (1)

(2)

(3)

5.32 0.04 5.36 8.81 0.59 9.40 0.57 0.12 0.54

5.13 0.02 5.15 8.13 0.71 8.84 0.58 0.13 0.56

5.00 0.05 5.05 8.48 0.72 9.20 0.55 0.12 0.58

77.3 MeV (4)

5.49

10.6 0.52 0.07 0.54

(1)

(2)

(3)

4.03 0.01 4.04 4.16 0.52 4.68 0.86 0.17 0.70

4.12 0.04 4.16 3.44 0.67 4.11 1.01 0.17 0.65

4.57 0.15 4.72 3.66 0.59 4.25 1.12 0.14 0.71

107.2 MeV (4)

4.97

3.57 1.39 0.06 0.82

127.3 MeV

(1)

(2)

(1)

(2)

2.98 0.01 2.99 1.71 0.44 2.15 1.39 0.21 0.72

3.54 0.05 3.59 1.41 0.61 2.02 1.78 0.19 0.70

2.42 0.01 2.43 0.95 0.34 1.29 1.88 0.22 0.75

3.38 0.06 3.44 0.84 0.58 1.42 2.41 0.20 0.72

D-state (3) Signell-Marshak 6.7 ~o D - s t a t e (ref. xT)). (4) Signell-Marshak 4 ~o D-state (ref. 21)).

644

A.

da)

DONNACHIE

= a(1+/51 cos

O)+b sin S 0(1+/~ 2 cos 0)

(13)

---- a + b sin2 0 + c cos 0 + d cos0 sin~0 and we m a y write a = aE+a~ t and similarly for b, c and d. The coefficients a, b,/~l(=c/a) and/53(= d/b) have been calculated using the Y.L.A.M. set of phase-parameters of Breit et al., and the corresponding transition amplitudes of table 1. The results together with the isotropy factor ~ ---- a/b are given in 3.0

1.0

0.5

0.3

~',,r(rob)

0.1

0.05

0.03 20

40

60

80 EF(MeV)

100

120

140

Fig. 1. The total cross sections. The theoretical curves are the following: present calculation 4 % D-state (solid line), present calculation 6 % D-state (dashed line), Signell-Marshak *~) 6.7 % D-state (dot-dash line), Signell-Marshak zz) 4 % D-state (double-dot dash line). The experimental points are the following: Aleksandrov et al. 33) (open circles), Allen ~2) (black circles), Barnes et al. 3o) (crosses), Galey 25) (black traingles pointed downwards), Halpern et al 3x) (black triangles pointed upwards), Hough =s) (open traingles pointed upwards), Waffler et al. 29) (black squares), and Whetstone et al. 24) (open triangles pointed downwards).

table 2, where comparison is made with the results obtained using SignellMarshak phase parameters. The total cross-sections are compared with experiment in fig. 1, the isotropy ratio in fig. 2 and the quantities/~1 and/52 in

PItOTODISINTEGRATION OF THE DEUTERON

645

fig. 3. In the latter case the experimental points are plotted as fl obtained from a best fit of the experimental data to the formula (da)~ o =

(a+bsin~O)(l+flc°sO)"

(14)

/-}1.0

o51

i

0.3

% 0.1

0.05

0.03

20

40

60

~'

80

100

120

ET(MeV)

Fig. 2. The i s o t r o p y ratio 0.8

o.6

a/b.

The curves and p o i n t s h a v e the s a m e m e a n i n g as in fig. l.

0.4

0

20

40

6o E~, (MeV)

80

100

120

Fig. 3. The quantities fll and ft.. The curves and p o i n t s h a v e the same m e a n i n g as in fig. 1.

646

A. DONNACHIE

The considerable increase of a R at low energies in the present calculations, compared to the value obtained using Signell-Marshak phase-shifts, can be attributed directly to the enhancement of E32 discussed above. It so happens that a E depends almost entirely on terms involving E32 , the other terms almost cancelling. Consequently a large value of E32 implies a large value of a E and vice-versa. Hence we get the above behaviour of a E at low energies. On the other hand, as the energy increases, the reverse situation holds i.e. aE calculated from Signell-Marshak phase parameters becomes greater than that obtained in the present calculations. The coefficient a M also differs considerably in the two cases at higher energies. This is a direct consequence of the smaller value for M 2 obtained in the present calculations compared to that obtained with Signell-Marshak phase-shifts. The values of bE and bM in all cases are very similar. As a result of this the ratio a / b found in the present calculations is greater than that of the Signell-Marshak results at the lower energies, but less at the higher. At energies below 70 MeV, the best fit to the isotropy ratio is obtained b y the present calculations with a 4 % D-state. This, however, does not give a reasonable fit at all above this energy. The best fit above this energy is given b y the Signell-Marshak results, but they, in turn, give too small a value at energies below 50 MeV. The best fit over the whole range is given b y the present calculations using a 6 % D-state, which lies intermediate to the other two. The total cross-section obtained with the present calculations with a 4 % D-state is too small above 80 MeV, but the other solutions fit reasonably well up to 130 MeV. The parameters/51 and/52 differ in the cases considered, but experimental accuracy is not nearly sufficient for any conclusions to be drawn. 3.2. L I N E A R L Y

POLARIZED

RADIATION

When we have partially or totally linearly polarized radiation, the crosssection is da d.(2

(d~Q) (1 + Z L ~,(0)sin2 Z), o

(15)

where X z is the degree of linear polarization and Z is the angle between the plane of linear polarization and the azimuthal angle of observation. The function Z'(0) is

with r :

bE--bM,

rp :

b/5 2 =

d.

(17)

To compare theory with experiment, the most convenient quantity is s :

bM/b E :

(b--r)/(b+r).

(18)

PHOTODISINTEGRATION

OF

THE

DEUTERON

64~

I

I

[

I

i

,.=

I

I v

E I v v ~o

1

I oo c~ Ct~

=k

..= v

cq~5 I

.= c~

648

A. DONNACHIE

The values of r, p and s obtained in the present calculation are given in table 3, along with the corresponding values obtained from the results using SignellMarshal< phase parameters. 3.3. POLARIZATION OF THE PROTONS The polarization of the outgoing protons for unpolarized radiation in the direction n---- p × k / I p × k ] is given b y (do') P ( O ) = s i n O C T o + T l c ° s O + T 2 e o s Z O ~

•

(19)

These coefficients are given in table 4. The differences between the present calculations and previous calculations are much more marked in the polarization parameters than in the cross-section parameters. Unfortunately at the moment there exist no experimental results with which to compare the theoretical values. 4. C o n c l u s i o n s It can be concluded that the Gammel-Thaler type phase parameters are as suitable for a detailed analysis of deuteron photodisintegration as the SignellMarshak phase parameters. The best fit to the angular distribution parameters at low energies is given with a low D-state probability, namely 4 %. However, to obtain a reasonable fit at photon energies greater than 70 MeV it is necessary to increase this figure to at least 6 % .The resulting fit at energies below 70 MeV is not so good as that obtained with the lower D-state probability, but is still fairly satisfactory. A low D-state probability is to be preferred on other grounds, in that the magnetic moment of the deuteron can then be explained without complicated inclusion of large mesonic and relativistic corrections 24). It m a y well be that retardation is of much greater significance than has hitherto been supposed 11,2o,21) as has been argued recently b y Matsumoto 18), and that a proper inclusion of relativistic corrections would allow the angular distribution to be fitted up to 130 MeV with a low D-state probability. The question of the correct deuteron D-state probability could well be clarified b y accurate experimental angular distributions in the energy range 15-50 MeV, for there the theoretical parameters differ b y up to 30 % depending on the D-state probability chosen. In theory, a complete set of measurements (angular distribution, polarization of the outgoing nucleons, angular distribution with linearly polarized photons) at one energy should suffice to settle the outstanding questions. To simplify the analysis, the energy chosen should be one at which a "unique" scattering matrix has been determined i.e. scattering energies of 68, 98, 150, 210 or 310

PHOTODISINTEGRATION

OF THE DEUTERON

649

../-'. \ .

~~.\/

16

I.I

14

\..\

/

12

10

/,

5

'\ \.

/,

'\

'\

•~

,k

30 °

60 °

90 =

120"

150,

180"

8(c.m,)

Fig. 4. T h e differential corss-section a t 52.3 MeV. T h e c u r v e s h a v e t h e s a m e m e a n i n g as in fig. 1.

I0 /

/"/

_,o - 30

.... _. \

"<~\

8(c,m.)

"2

! "%'-.~ ---~/'

Fig. 5, Proton polarization at 52.3 NIeV. T h e curves h a v e the s a m e m e a n i n g as in fig. I.

650

A.

DONNACHIE

MeV, corresponding to photon laboratory energies of 37, 53, 78, 107 and 158 MeV, respectively. The energy 158 MeV is too high, for at this energy relativistic corrections and the inclusion of mesonic effects are necessary; 107 MeV is probably too high also, at least until the question of retardation is settled. At the other end of the scale, 36 MeV is too low for reliable polarization, measurements to be made, as probably is 53 MeV. This leaves 78 MeV as the most suitable energy for the present. 10

L. ~

6

a~

4

30*

60"

90 °

120e

150"

180"

e(c.m.)

Fig. 6. T h e d i f f e r e n t i a l c r o s s - s e c t i o n a t 77.3 M e V . T h e c u r v e s h a v e t h e s a m e m e a n i n g a s in fig. Io

10

/ f ~

"x.

~I / . ~ ,- / ,

/.--'--

--"

3~)o "

\ ",

6 0'.~~l.' y .

eC . . . . )

90'

1'~O"

1.50"

180)/

-~0 P(°I,) -

20

Y,X,',

/,/

y

,/,'/ • t+

/,

-30

Fig. 7. P r o t o n p o l a r i z a t i o n a t 77.3 MeV. T h e c u r v e s h a v e t h e s a m e m e a n i n g a s i n fig. 1.

P H O T O D I S I N T E G R A T I O N OF THE D E U T E R O N

651

In figs. 4, 5, 6 and 7 we give the different theoretical predictions for the angular distribution and proton polarization at photon energies of 53 MeV and 78 MeV. The author gratefully acknowledges the award of a Research Studentship from the Department of Scientific and Industrial Research. References 1) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

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