DETERMINATION OF THE TRANSITION AMPLITUDES OF THE D(d,n)3He AND D(d,p)3H H REACTIONS FOR Ed≤500 keV

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DETERMINATION OF THE TRANSITION

AMPLITUDES OF THE D(d,n)3He AND D(d,p)3H H REACTIONS FOR Ed ≤ 500 keV

S. Lemaître, H. Paetz Gen. Schieck

To cite this version:

S. Lemaître, H. Paetz Gen. Schieck. DETERMINATION OF THE TRANSITION AMPLITUDES OF

THE D(d,n)3He AND D(d,p)3H H REACTIONS FOR Ed ≤ 500 keV. Journal de Physique Colloques,

1990, 51 (C6), pp.C6-463-C6-466. �10.1051/jphyscol:1990653�. �jpa-00230923�

DETERMINATION OF THE TRANSITION AMPLITUDES OF THE ~ ( d , n ) ~ H e AND D(dt P

l3

H H REACTIONS FOR E,S500

J&v

S.

LEMATTRE

and H. PAETZ GEN. SCHIECK

Institut fiir Kernphysik, Universitdt Ktiln, 0-5000 Ktiln 41, F.R.G.

Resume

-

Nous analysons toutes les donnees experimentales des deux reactions de fusion D ( d , n j 3 ~ e e t ~ ( d , p ) ~ H avec des energies de moins d e 5 0 0 keV. Les ondes S jusqu'a D sont consider6es. Les elements de matrices de toutes les 16 transitions sont obtenus par une minimisation de x2. On n'observe aucune suppression des transitions des etats quintet dans le canal initial e t c'est pourqoui la suppression des neutrons dans la .fusion polariseen est improbable.

Abstract

-

An analysis of all available experimental data of the mirror fusion reactions

~ ( d , n ) ~ H e and ~ ( d , p ) ~ H below 5 0 0 keV is presented. Account is taken of S-, P-, and D-waves in the input channels of the reactions. All 16 participating transition amplitudes are obtained b y a fit to the experimental data. In accordance with refined resonating group calculations no suppression of quintet entrance-state transitions and therefore no neutron suppression in "polarized fusion" can be derived.

l - INTRODUCTION

Due t o the unusual properties of the t w o D+D fusion reactions ~ ( d , n ) ~ ~ e and D ( ~ , ~ ) ~ H and in v i e w of astrophysical and possible fusion energy applications the knowledge of the transition matrix of these reactions is of special interest. For these t w o reactions a large body of experimental data of different types of observables exists at projectile energies below 5 0 0 keV. Most of the data result from experiments with incident polarized deuterons on unpolarized targets. For the investigation of special questions, such as the possible suppression of D+D neutron production in fusion energy devices, polarization correlation or polarization transfer measurements would b e preferable but have not been done yet. The task of extracting the transition matrix from existing data meets the difficulty that 16 transitions have t o be considered since D-waves appear already significant above 150 keV.

Up t o the present different approximative approaches t o a theoretical description of the D+D reactions have been undertaken. These include a simple potential model /1,2,3/ where the energy dependence of the transition ainplitudes TB,(E) is assumed to be governed solely b y Coulomb and centrifugal barriers in the entrance channel. The present calculations are based on this model. Furthermore there are an R-matrix pararnetrization approach /4,6/, DWBA calculations / 7 , 8 / and resonating group (RRGM) calculations / g / . Only recently microscopic 4-body (Faddeev) calculations have been performed for the four-nucleon system though with very limited complexity and without taking Coulomb forces into consideration /10/.

(4)

This work has b e e n funded b y the German Federal Minister for Research and Technology (BMFT) under the c o n t r a c t numbers 06-OK-153 and 06-OK-272

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990653

COLLOQUE DE PHYSIQUE

2

-

^METHOD

in this study all relevant transition matrix elements for both reactions have been determined b y a straightforward least-squares fit on the basis of all experimental data /11,12/ (for a discussion o f the experimental situation see, e.g., ref. /13/). Most o f the information w a s obtained from experiments with polarized particles including recent extensive measurements of the vector and tensor analyzing powers for both reactions 112, E.Pfaff, private communication/.

In the above-mentioned potential model the transition amplitudes TBa(E) factorize like:

(1) TBa(E) = CeJE) fBu

The amplitudes TB, do not depend on energy and the Coulomb functions Ce,(E/ are calculated for an interaction radius of 7 fm /l/. The absolute values of the penetrabilities for incoming S-, P-, and D-waves are shown in figure 1.

0 100 200 300 400 500

Elab fieM

Fig. 1

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Absolute values of the penetrabilities Ce (E) for 4 =0,1,2

The experimental data enter the calculations as Legendre expansion coefficients a$ of the angular distributions of the observables A ' ( E , ~ ) :

(2) A ' ( ~ , 8 1

- ¹

^{a \ (E) P;} ( c o s 8 )

e

The observables are bilinear functions of the transition amplitudes:

( 3 ) A ) ^W

1

b i ( R e ) ( ~ m ~ ; ) ~ i ( c o s 8 ) m n t mn Im

( 4 ) thus

A unique set of reaction matrix elements Tm w a s found b y fitting the expansion coefficients a; (E) according t o eq. (41 t o the experimental m e s . The fits were performed b y means of a derivative-free form of the Levenberg-Marquardt algorithm (for more details see ref. /14/).

3

-

^RESULTS

In table 1 the absolute values of the resulting 16 energy independent transitions TB, are shown.

According t o their orbital angular momentum t, they have to be multiplied b y the penetrabilities ICc,l when comparing their respective influence on the observables such as cross sections.

W e learn from table 1 that the quintet transition amplitudes < 5 ~ 2 2 ' 1 ' ~ ~ ) and <5~212+13~,>

are of the same order of magnitude as the singlet transition

<'so ~ o " s ~ > ,

which rules out the possibility of a neutron-lean fusion reactor b y polarizing the nuclear fuel. Our results

with the energy dependent penetrabilities Ctu(E) (see fig. 1). The notatlon is: =

<

ⁱⁿ

I I

^out

>

⁼

<

^2sa'ltaJ

I J " [ ~ ~ P ' ~ ~ >

The errors are specified in parentheses

B J

Table 2

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Relative S-wave quintet state transitions of the ~ ( d , n ) ~ H e reaction compared t o RRGM results at Elab = 8 0 keV

e.g. for the S-wave quintet transitions agree reasonably well with RRGM calculations / 4 / (table 2 ) . Furthermore the results are in qualitative agreement with an R-Matrix analysis / 6 / but contradict strongly the DWBA calculations of Zhang et al. / E / .

From the knowledge of it is possible t o predict all observables which have not yet been investigated experimentally. Below, for both reactions the predictions for the polarization transfer observables TI1 11 and T; are shown as an example For the D(d,n) reaction T;; is in agreement with a qualitative observation of Janett et al. / 5 / . At Elab= 4 6 0 keV, aIabW 90°,1100 they found polarization values 5 15%.

Fig. 2 - Polarization transfer observable Tll 11 for ~ ( - d , z ) ~ ~ e and D(~,;)~H calculated with the reaction matrix TB= (E) (eq. (1))

COLLOQUE DE PHYSIQUE

Fig. 3 - Polarization transfer observable T:; for D(;,:)~H~ and ~ ( 2 ~ 5 ; ) ~ ~ calculated with the reaction matrix T (E) ( e q (1))

B a

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