-THE AUSTRALIAN NATIONAL UNIVERSITY

RESEARCH SCI-~OOL OF PEYSICAL SCIENCES

DEPARTMENT OF THEORETICAL Ph'YSICS

Professor and Head of Departraent

Professor

Professorial Fellow

Senior Fellous

ANNUAL REPORT 1968

Sta:f:f

JCJ. Le Couteur, M.A. ,Pl~ .D. (Cantab. ;FAA

D.C. Peaslee, A.B.(Prin.), Ph.D.(MIT )

F.C. Barker, M.Sc. (Melb.) ,Ph.D. (Biro.~

X. Kuraar, B.Sc.(Agra ~ , l1I .Sc.(Alld. ) Ph.D. (rncM.)

W.S. Woolcock, B.Sc. (Qld. ) ,Ph.D. (Cantab.) ( froriJ July 68)

B.A. Robson, M.Sc.,Ph.D.(Melb.)

: L. J • Tassie , M. Sc • , Ph. D. ( Me 1 b • } (from Dec 68)

Senior 3esearch Fellow S. Mukherjee, M.Sc.,Ph.D.(Calc.)

Research Fellows

Research Students

Attached

Visiting Fellows

R.C. :;Ie::-medy, B.A. ,M.S. (Mich. )Ph.D. (~-Tash.) (to May 58)

R.J. Baxter, M.A. (Cantab.) ,Ph.D. (Al-JU) (to Aug 68)

S. Furui, H. Sc. , Ph.D. (i-Iokkaido)

C.A. Edvi-Illes, B.Sc.,liI.Sc.,Ph.D.(Eelb.) (from Sept 68)

s.c. Gupta, M.Sc. Eleanor ~-J. Walsh, B.Sc. H. IT. Trofi!:lenkof'f, I-1. Sc. D.M.M. Bedford, M.A. B.M. Fitzpatrick, B.Sc. II. 1~unar, H. Sc. W.I. a obertson, ~.Sc. G. Delic, B.Sc. G.D. Swith, B.Gc.

{to Feb 63)

(from Jan 68 ) (from Dec 53 1

P.B. Treacy, l1l .Sc. (Sydney) ,Ph.D. (Cantab.) (Reader in Nuclear Physics ANU)

(from A:pl £8)

Professor Y.R. Wagh:oare (Indian Institute of' Technology, Ka.npur)

(May-June 68)

Dr R.J. Hosking (The Flinders Unive=sity o:f South Australia) {Aug 68 to

Jan 69)

Staff Hatters:

There were numerous staff changes during the year. The

departraent was strengthened by the appointncnt of two Senior

Fellows: Dr Woolcock. and Dr Tassie, and Dr Robson was proaoted

to a Senior Fellowship. Also, Dr Treacy, Reader in Nuclear

Physics, ,'las attached to Theoretical Physics for one yea:r.

Study Leave:

Professor Peaslee was on study leave from July 1968, and

visited i;:rntitutions in Europe before s:pending most of hi:::;

leave at t:"-e r'1assachusetts Institute of' Tec:U1ology.

Dr K. Kunar was on study leave frora April 1968, and

visited Universities in India anG Moscow before settling dO"i,ln

for two ter~s at Oxford.

Research ?rogranne:

Ti::e Department of 'l'}1.eoretical Physics continued to work

on funcaraental probleas of nuclear physics, elementary particle

physics , statistical n:cc:1.anics and plasraa physics . Sooe of

the work is related to the experiuental interests of the School

and during the year there was close collaboration with tl":e

Departaent of nuclear Physics on problems of nuclear structure

and reactions.

+ 8 Huclear Physics: Properties of the 2 states of :r.Je below

the 7Li+p threshold have been obtained by 2-matrix analysis of

data fror.i a-a scattering and various reactions. A second broad

2+ level at about 9 lfoV excitation energy is ir.iplied, and its

~resence causes uncertainty in the parameter values of the 16. c

and 16.9 MeV levels. ~ata from the 7Li(p,a) 4He reaction

obtained with both pol~rized and unpolarized protons are being 8

analysed to determine the properties of levels of Be in the

20 l.foV :.:-egion.

A general computer progrararne has been developed to construct

non-s?urious shell model basis states of non-normal parity for

nuclei ,,ith A= 4-16, and to obtain eigenenergics and eigenfwictions

fo~ a given interaction between nucleons.

An a?parent regularity in the energy differences of

corres?onding levels of oirror nuclei in the 2s-ld shell is being

investigated.

-2-

The effect of possible tensor forces in the deuteron­nucleus interaction on DWBA calculations for deuteron stripping has been studied fort= l transitions in the 40ca(d,p) 41ca reaction. The j-dependence of the cross sections and vector analysing powers has been investigated.

The j-dependence of the cross sections for several transitions in the 5°cr(d,p)51cr reaction is being studied.

The m,raA analysis of the reaction lL1n(d,p) 15N at low deuteron bombarding energies, taking into account compound­nucleus fornation in the Hauser-Feshbach approxioa.tion, has been cor.1:pleted.

The 12c(d,p) 13c reaction at 5-10 MeV deuteron bombarding

energies has been analysed using the distorted-wave and Hauser­Feshbach theories.

The tensor polarization of deuterons scattering is being studied.

in 16

0-d elastic

The deuteron tensor polarization for the reaction 9Be(d,d) 9Be is being investigated.

The j-dependence of several£= l transitions in the lp shell is being studied.

The j-dependence effect is being used to assign spins to residual states in the reactien 54cr(d,p)55cr.

Work. was completed on the construction of a Regge type representation for partial wave scattering amplitudes. Satisfactory results were obtained over a large energy range for the case of a Yukawa potential strong enough to have a pair of bound states or resonances. Another application was to the description of optical-well scattering of low energy neutrons on nuclei.

A very satisfactory description of the deuteron optical­well in tercs of nucleon-optical-wells was obtai.."1.ed using Feshbach's definition of the optical well: the present theory recoves the 6iscrepancy in the real and imaginary parts of the deuteron-optical-well noted by other authors.

Calculations are in progress on the time-delay in nuclear scattering and reactions using a time-dependent form of Schrodinger wave function and the definition of time delay given by Watson and Goldberger. We expect the result for time delay to be very much different frora the old result of Wigner in terms of phase shift, particularly when the potential is strong enough to support bound states and resonances.

-3-

An oxperi~ent on the beta-decay of boron-8, previously

carriecJ out in the nuclear Pl1.ys ics Departr::ent , has been analysed + 8

using R-matrix theory , in terws of 2 states of Be . This

work is being ?repared for publication .

The analysis of a-a elastic scattering has been studied

with various potentials, and their ~ole structm~e and pole

representations investigated . A static singular potential

was found which describeG the 1:nown data well, and has a

reasonably- convergent Cheng-type representation .

A flexible optical- nodal ty?e progra~oe has been developed

to handle a variety of types of potential , both ordinary and

singular , and also coupled-equation aethods for higher-order

equations . The programme allm.-,s any real or complex angular

monentun , and :perr.ii ts coc::putation of angular-nomentun (Rogge,

poles . It incorporates subroutines for con~lex gamma functions ,

Coulor.ib f'u.71.ctions for complex angular r:1or..10ntun and certain

1-Thi ttake:..~ functions used wi t:t: Gingular potentials .

Another prograrnae has been 11rittem to cal c ulate .aegge-pole

r epresentations in produc t forn , i . e ., Cheng and aodified-Cheng

representations . This includes subroutines for cooplex

psi-functions and Gaussian hy~ergeometric fl.uLCtions .

Solutions to the Betne-Salpctor equation in the

instantaneous a~proximation have been studied , using the above

conplcx equation techniques . Scattering solutions are being

studied , wit:1 e:::phasis on properties of ' daughter ' pole

trajectories and 1 abnorl:la.l 1 solutions .

Eleoontar y Part icle Physics : The boundaries of the

doubl e spectral func tions in t:i.1e Ma.ndelGtam representation have

been calculated for a large nu.Jber of hadronic proc esses , us i ng

onl y elastic unitarity and ' extended' nnitarity . This has l ed

to interesting problems concerning anonalous thresholds ; can

one see how they arise without resorting to partic ular d i agraos?

A calculational progra::me is also continuing for the

deternination of coupling c onstants and low energy parameters

of the pion-nuc leon and kaon-nucleon syster:1s .

The path integral aethcd was used to investigate the

' classical field approxi~ation' to quantized field theory.

An extensive study ,-,as r.1adc of non-l0ptonic hyperon

~ccays fro~ the point of view that the interaction consists

of a ~roduct of Cabibbo cu~rcnts. Two cethods of calculation

were co:ploycd; one using the current algebra oethod , the other

treating hadrons as non-relativistic bou..-i-id states of qua:.~!:s .

A good f'i t to the expcri;:1cntal a u yli tudes cannot be obtained

when su3

syr.rr.1ctric values arc ci:.osen for t h e coupling constant:,,

but it is ::_:)ossiblc to reproduce t:i::e an;,litudes by including

contributions fron baryon resonnncos in a ;iole approxir.1ation , ':) · --( p - +,

Ou- results indica to that resonances wit~,. J.! = ·2 J = "2 i :}lay

a nore i:.:::_:)o:.~tant role in s-11avc L::>-wavc ) decays than resonances

. - r - +( P - --, wit~ J = 2 J = 7 J • Using c;_uark r..,.odcls , it was fowid that

the single and two quarl~ t:ra:~G it ions yield a,..:~.Jli tud.os that

satisfy the Sugawara-Suzuki su.:.: rules de:;.~ived f:..~o;:1 curron-t

algebras. 'I'l:c two qu2.r~t transitions ~:ial-..c i::1?ortant

cont~i~utions to the ex?ericcntal a s ~litudos .

~Tork continued on the fo~~-dioensional =c?resentation of

scattering aoplitudos and its relation to expansions in terus of'

crossed cha::i.~cl variables. A r.10difica tion to the usual

O(J,l~ analysis was introduced and single :;_)olo , single j value 0

contributions to the differential cross sections for pp, TTp,

- 0 * * -TT p -> TT Y), TTT'J -> WN , TTIT -> Y)IT , ITU ""' YY wore calcula tcd and

c o:::1pa::-ed vri t:1. cxperir.1ental data. ~ith this representation

di:;,s in tl-:e experir:wntal cross sections appear naturally at

about the :right values of r.::occ~tw:-: transfer.

Statistical Ne c hanics anc. Plasna.s ; It was shown that the

?ercus-Yevic.: approximation for the radial distribution fwiction

can be solved analytically for a model gas consis ting of hard

spheres ,,it·! surface adhesion. The results show a first order

Van de11 ~-Taals phase transition w~1.i c h ap::;:iears to be of the ty:::>e

found m.u:,erically wp.en tl-:e inte:::-action is represented by the

Lennard-Jones 12- 6 potential. The solution was much simplified

by a9;ilying the 1-Teiner-::opf technique to the solution of the

Ornstein-Ze:::--nike relations and it is thought tl:.at this method

can be a??iied to other aodels in statistical ~echanics.

A cl.,.apter on Distribution Functions ,-ms written , by

invitation, for an Acader.1ic ?ress boo:{. ':?hysical Chemistry'•

Studieo lave been cade , in the Vlasov approxiaation, of

plasna in a cylindrically sym::ietric magnetic containing field.

-5-

The influence of magneto-viscosity on plasma stability

has been considered . Cocplete stabilisation of the resistive

- g instability at sufficiently high temperature is predicted

from ap?ro?riately generalised ~ydromagnetic theory . In

contrast, the (ideal) hydro1:1agnetic g:cavi ta tional mode is

rendered overstable . ~~cse results nay be relevant to ttle

bel.aviou::- of the AIJU torus.

Otner Activities :

?rofessor Le Couteu:.~ , .Jr :::u:-.1ar and D:.:- :2.obson read :::;,a:::;,ers

at AIIZAAS Conference in Ch:::'istc:i1.urcl1., ITew Zealand .

The departoent also contributed five pa~ers to the

AilTSE lJuclear Physics Conference at Canberra in February .

Dr Robson accepted an invitation to deliver a series

of lectures at Flinders University .

Spea:C..e:.~s at our regu.lar se":1inars included the following

visitors f~om other Universities:

Professor H.S . Green

Dr Boris Castel

Professor Y . R. . ~!aghcare

Dr B . Ninham

Professor J . C. ~ard , Fas

Professor I . McCarthy

Dr R . B . Leipni::

Dr R . J . Elliott

Adelaide

Queens University , Canada

Indian Institute of Tec:b.nology, l~npur , India

n . s . -:il . I~cquarie

Flinders

Adelaide

Oxford

-

Barke!' , F .C. and Fitzpatrick, B. M.

Barl~er , F . C. , "f !·ia y , H • J • , l Treacy , P . B .

* Baxter , ~ .J.

Bedford , D.E.

*

Cords, =~. , Din , G, U., Ivanovic!"1., ii . , Robson , :B .A.

Davids on, l-1 . G.

Furui, S. and + Fujii, K , +

+ + + +

Furui , S., Tsuchida, T . ,

Fujii, Z . ,

+ Y..awasaki , S . +

* I~ennedy , R . C.

f'.iumerjee , s .

-6-

?ublications

' R- ;:1atrix fit to 93e(Y , n)8

Be cross section nea!' threshold' , Aust.J.Phys. ?l , 415 .

'O+ States of 8Be' , Aust .J. Phys . 21, 2J9.

'Th re e - ? article hyp er-netted chain appro:;cir.iation' , Ann.Phys. ll£, 509.

' The ~ressure in the Percus-Yevick approxi2ation', J.Chem.?hys. !±1., 4355 .

' Dimers on a rectangular lattice' , J . Ea t h . ?h.ys • .9.., 6 50.

'Ornstein --Zernike relation for a disordered fluid', Aust . J . Phys . 21, 563.

' Percus-Yevick equation for hard sphe~es with surface adheoion', J .Chem. Phys • .!±2. , 2770 .

' :iJistricut ion Functions , C!1apter 4 i_:n, Physical Cheu1L:;try : An Advanced T:.~eatise . Vol. VIII . (Acade~ic Press , New Yor~ ) .

' On ' ~ oost' natrix elec ents' , Huovo Ci::1ento j..J. , 804 .

17enso~ polarization of deuterons froa 12c-d 1

, nuclear Phys . A-ll.J. , 608.

' Bloc king effect s in tile asymr.1etric rotor aoael ' , Huclear ?hys. AlOJ, 427.

'Pion decay of cesons in the baryon­antibaryon mocel', Ann.Phys.~' 12.

'Conoent on interrelation between weak four-fer.:::1ion interaction and weak bilinear interaction' , Prog . Theor . Phys . lLQ, 571 .

1 0 n nonleytonic decays : A possible schP-ne for J*-J-type \'Teak interaction p icture ', Prog.Theor.Phys. 1.2., 1278.

' Pairing correlations in nuclear matter A self-consistent calculation ', Hue lea:;,." Ph ys. All8, 189.

'Op tical potential for deuteron', Nuclear Pl1.ys. All~, 423 .

+ *

*

, ,

+

Mukherjee, S. and Shastry, c.s.

Nakagawa, H.

llal'..agawa, M. and Troficenkoff, N.N.

Nurzynski, J., Bray, K., Robson, B.A.

Peaslee, D.C.

Robson, B.A.

·waghoare, Y .R.

-7-

'Scattering amplitudes generated by pole terr.1s of' Regge-type representations', Phys.~ev. 169, 1234.

'A quark nodel and soft pion emission in leptonic decays of mesons', Uuovo Ci.::1ento -5.!i.A, 723.

1 S-wave nonleptonic hyperon decays and nodels of baryons', Huovo Cicento ~. 951.

'5-wave nonleptonic hyperon decays and models of baryons', Nuclear Phys. B~, 93.

'The 27At( 3He,a.)26

A.t reaction at 10 MeV bombarding energy', Nuclear Phys. Al07, 581.

':tlote on high-pT events in cosmic rays',

Nuovo Cimento .5.5.B, 562.

'(d,p) spectroscopic factors from the Butler-Born approximation', Phys.Rev. 171, 1208.

'J-de~endence for 2p neutron transfer in ld,?i reactions', Phys.Letters 26B, 501.

'Theory of nuclear structure', lecture notes 1968. AllU publication (mimeographed).

** 'Woolcock, w.s. 'Asynptotic behavior of Stieltjes Transforras II' , J .I{ath. Phys • .2., 1350.

Ph.D. Thesis - Approved

Gupta, s.c. 'Transport coefficients of binary gas mixtures', (1968), pp. 219 + x.

* , t

**

Based on work done while a member of the Department of Nuclear Physics.

Former rneciber. Based on work done while a member of the Department.

A member of the Department of Nuclear Physics.

Hot a member of' this University.

Based on work done prior to joining this University (a substantial amount of' work and compilation having been done at this University).