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born 13 Sept.1924 (died 25 June 2010)the son of a noted Welch preacher, the Rev. Harold Flowers and his wife Marian in Blackburn, Lancashire
Before he was 20 he was recruited by John Cockroft to the Anglo – Canadion atomic bomb project at Chalk River, Ontario
Cockroft brought him back to Brittain to work in Otto Frisch’s group of the Atomic Research Establishment at Harward in Fuch’s theoretical section
in 1946
in 1950
Fuchs was arrested as a Soviet agent and Flowers went to Birmingham University to work under Rudof Peiersls
in 1958 (till 1967)
he was appointed professor of theoretical physics in Manchester University at the age of 34
in 1961
elected as a fellow of the Royal Society (FRS) at the age of 36
in 1964
in 1973
(till 1985)
Chairman of the Science Research Council (SRC)
Rector of Imperial College of London University
in 1985 - 1990
in 1969
in 1979
Vice-Chancellor of London University
He was knighted (Sir Brian Flowers)
Lord Flowers of Queen’s Gate
President of the Institute of Physics President of the European Science
Foundation President of the National Society
for Clean Air President of the Parliamentary
Scientific Committee Chairman of the House of Lords
Selected Committee on Science and Technology
Chairman of the Royal Commission on Environmental Pollution
Officier of the (France) Legion d’Honneur
Meantime
, Proc. Roy. Soc. A 210 (1951) 197 Proc. Roy. Soc. A 212 (1952) 248
Group – theory classification of nuclear shell states
Link between results (a and b)
(a - 1952) (b - 1964)
and
(b – 1964)
, Proc. Phys. Soc. 84 (1964) 193, Proc. Phys. Soc. 84 (1964) 673
Group structure
for example: , n =8 ,
N=12.870 2
7j
24 jSU )2()12(12 JJ SUjSpjSU
)2(TSU
n
jN
24
Infinitesimal operators
JTaa )( )0,1()0,()0,( )()()( aaaaaa oddJJ
)1,0()( aa
Resulting states
)()..()..(; 021 JJstnTj n
),(
),(
),(
)(
)(
)(
TJ
TJ
TJ
aa
aa
aa)0,1()0,( )()( aaaa oddJ
)1,0(
),0(
)1,0(
)1,0(
)(
)(
)(
)(
aa
aa
aa
aa
T
)48( jSO)2()12( JSUjSp
)2()5( TSUSO
00 ,, JJTTnst
In the new basis – diagonalization of the pairingHamiltonian:
)1(2)1(2)
2242()(
4
1ttTT
snjsnGE
the classification of l nuclear configurations was also given in the new qausi – spinclassification:
Moreover:
n
)(
)(
)(
)(
)(
)(
LST
LST
LST
aa
aa
aa )0,0,1()0,0,( )()( aaaa oddL
)0(
)0(
)0(
)0(
)(
)(
)(
)(ST
ST
ST
ST
aa
aa
aa
aa
)010()( aa
)001()( aa
)416( lSO)3()12( LSOlSU
)4()6()8( SUSOSO )2(SSU
)2(TSU
with energy diagonalization :
)2()4()4
1
4
144)((
2
1 '' PPPPsnlsnGE
22 '')2'(')4('' pppppP
born 17 July 1929 (died 21 October 2008)in Gospart, Hampshire of an engine driver and schoolteacher
He read mathematics at University College Southampton, graduating in 1949 and remaining to do postgraduate work
He obtained his doctorate in theoretical nuclear physics under the supervision of Hermann Jahn.
He joined the theoretical division of Atomic Energy Research Establishment in Harwell when Dr Brian (later Lord) Flowers was appointed director.
After a year in the USA at the University of Rochester he returned to Southampton.
In 1962 he moved to the School of Mathematical and Physical Sciences at the new University of Sussex , Brighton, remaining there until his retirement in 1994.
Phil Elliott achieved global recognition in 1958 with the publication of an application of the symmetry group SU (3) to nuclear structure.
This work become one of the most frequently cited references in the field.
In 1998 – in the 40th anniversary of the SU (3) model – a nuclear physics conference held in Brighton with over 100 delegates from over the world.
The conference began with keynote talks by Phil Elliott himself and Akito Arima on the origin and development of the SU(3) model.
The advent of the Interacting Boson Model of nuclear structure introduced by Arima and Iachello gave his research new impetus in establishing a firm connection between it and more familiar shell model.
This aim was achieved in series of papers in 1980’s on neutron – proton pairs and isotopic spin in collective nuclear motion.
Phil Elliott was elected to the Royal Society (FRS) in 1980.
In 1994 he was awarded The Rutherford medal and prize by the Institute of Physics.
In 2002 the European Physical Society awarded its prestigious Lise Meitner prize jointly to Elliott and Iachello „ for their innovative applications of group theoretical methods to the understanding of atomic nuclei”.
(a) The famous SU(3) Elliott model and
(b) The Interacting Boson Model: IBM 3
and IBM 4
Link between (a) – 1958 and (b) – 1980: the symmetry consideration with group theory methods
(a) , Proc. Roy. Soc. A 245 (1958) 229, Proc. Roy. Soc. A 245 (1958) 562
(b)
, Phys. Lett. 97B (1980) 169
, Phys. Lett. 101B (1981) 216
, Nucl. Phys. A 435 (1985) 317
NOSC EH
N = 0,1,2,... = N, N-2,..., 0 or 1
)2
3( NEN
For a given N there is a (N +1) (N+2)
multiplet of states with the same energy .
NE
l
Conclusion: there must be a higher symmetry then SO (3). It is the famous
Elliott’s symmetry SU (3).
and
)2(2
1
0
6
1)(
2
1)(
2
3)(
OSC
Q
L
H
l
0,, qq QHLH
'',qqqq LLL
'',qqgq QQL
'',qqqq LQQ
Elliott proved then the nine operators H, L , and Q form a basis for Lie-
algebra of the U(3) unitary group and
U(3) = U(1) SU(3)
This is the famous Elliott’s SU(3).
(L , Q ))( OSCH
Under the same symmetry group SU(3) we can consider the mixing configuration of states belonging to the same IR of SU(3) on different l – shells as Elliott in his original paper considered for N=2 and 2p and 1f shells.
Main assumption of Arima and Iachello:In even nuclei for ground and low excited states nucleons form pairs coupled to lowest J only ,i.e. J=0 and J=2
2,...,1,2)(
)(
2
0
bosondaa
bosonsaa
J
J
, , and
form a 36 – member set which can be considered as the infinitesimal generators of the U(6) unitary transformation group.
Then, the operators
ss sd ds
dd
The full application of the IBM model follows the description of different multiples of atomic nuclei with the help of symmetries starting with U(6)
To make the model more realistic, Elliott introduced to IBM the isospin labels:
(T=0 is not allowed)
TMTs ,1 and
TMTd ,1
Then the operators
are generators of the symmetry group
U(18)> U(6) U(3)
That is the starting point of the ElliottIBM 3 model
TIss ,0)( TIds ,2)( TIsd ,2)( TIdd ,)(
and ; S=1,T=0 or S=0 T=1
To include T=0 to bosons, Elliott introduced the intrinsic spin to bosons:
STs
STd
The symmetry starting group, the IBM 4model, is
which is the Elliott IBM4 model
)6()6( STL UU
With these models Elliott was able to
analyse the neutron – proton on lor j
shell configurations.
Thank you for your attention
