Nuclear Surface Unveiled by Knockout Reactions. Arun K Jain
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Transcript of Nuclear Surface Unveiled by Knockout Reactions. Arun K Jain
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Nuclear Surface Unveiled by Knockout Reactions.Arun K Jain
Nuclear Physics Division, B.A.R.C., Mumbai.
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N-N Interaction has a complicated nature ( provided to it by the strongcoupling finite mass mesons), it has strong short range repulsion (almost a hard core of ~ 0.5 to 0.6 fm) and a finite short range, but a comparatively longer range, ~2 fm strong attraction.r
VNN
For structure most of the N-N interaction leads to the mean field of finite range Woods Saxon type. rNA
VNA
This longer range residual interaction leads to clustering
Clustering due to long range residual interaction
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p0
p1
p2
q1
q2
pB
Knockout Reaction Kinematics
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a’
bIncident momentum k1
Knockout ReactionA(a , a ’b )B
1k
1'k
2'k
21 '' kk
21 '' kk
2'k
1'k
1q
2q3k
3211 '' kkkk
1k
a
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If b were free then k3 = - k3 = 0
E1=E’1+E’2
If the particle is bound by a few MeV, then E0=E’1+E’2+Q
as the Q is (- ve ) E’1 and E’2 are < E1 and E2 respectively. Hence k’1 and k’2 are < k1 and k2 respectively. and θ1 and θ2 of k’1 and k’2 will be slightly < that of free scattering.
211 '' kkk
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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Zero Range Knockout
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2
121
3
)(QTddSKF
dEddd LJ
BAab
LJ
From Transfer Reactions one obtains reasonablerelative spectroscopic factors.
For Knockout Reactions one uses quasi free scattering approx.or Distorted Wave Impulse Approximation (DWIA ).
(a,2a) , knockout reaction cross section = product of kinematic factor, a-a Cross section and Distorted wave form factor, (~Fourier transform of Wfn).
.)(),(),(),()12( )()()(2/1 **
RdRRkRkRkL LJaAaAbBbBaBaB
)(QT LJBA
SLJ is the cluster spectroscopic factor for specific L and J.
The transition amplitude may be written as :
Here = B/A.
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Ea So+ σPW / σDW
Theory 0.23 -850 MeV < 1.8 5.490 MeV 15 ~1500
52.5 MeV 150 ~3200
Ground State spectroscopic factors Sα for 16O(α, 2α)12C
139 MeV 200 MeV Ratio17 0.48 35
Theory 0.55 0.55
Ground State spectroscopic factors Sα for 12C(α, 2α)8Be
at 139 MeV and 200 MeV
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Reaction θ1-θ2 P3 (MeV/c) Spectroscopic factor (Sα)
16O(p,pd)14N 40.10-40.00 ~41 0.4316O(p,pt)13N 40.10-40.00 ~51 3.416O(α,αd)14N 9.00-43.990 ~4 5516O(α,αt)13N 25.810-
43.990~13 53
16O(α,αt)13C 25.810-43.990
~2 55
Discrepancy between Proton and Alpha inductedCluster Knockout Reactions
Here Spectroscopic Factor Sα is seen to be almost
~2-orders of magnitude too large
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Finite Range Knockout
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Knockout using Short Finite Range Repulsion
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Zero Range Approximation for the knockout vertex is hidden in the conventional language of the factorization approximation of the knockout vertex matrix element.
Actually the transition matrix element and the double differential cross section are written as,
BBLAABBaBaB
ifLfi
RdrdRrkrtRkrk
drrgkkT
212211)(
0121222)*(
2)*(
1 )(),()(),(),(
)(),(
a
2
121
,3
),(..
if
Lfi
LJkin
JL
kkTSFdEdd
d a
a
Which includes the finite range effects, which we have worked for the first time.
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t- matrix effective Interaction
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t-matrix:- Vt
)ˆ()(
)12()(4,2,0
rPekrkru
lir lil
l
l laa
The Moller wave operator is such that it transforms the plane wave states, into scattering states, is defined in terms of radial scattering solutions ul(kr) as:
...4,2,0
)ˆ()(
)12()(),(l
lill
likz rPe
krkru
lirVerEt laa
ml
mlLim
mll
lL dPPPemikrjkrkrLirVLrEt l
,
1
1
* )(cos)(cos)(cos)(cos)12())(()()12()(2
12),( qqqq
Arun K Jain & Bhushan N. Joshi, Prog. Theor. Phys. 120 (2008) 1193
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171
Repulsive core + Attractive α-α t-matrix, tψ=VФ
Arun K Jain & Bhushan N. Joshi, Prog. Theor. Phys. 120 (2008) 1193
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172Arun K Jain & Bhushan N. Joshi, Prog. Theor. Phys. 120 (2008) 1193
Attractive α-α t-matrix, tψ=VФ
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173
d/d from Attractive a-a potential
Arun K Jain & Bhushan N. Joshi, Prog. Theor. Phys. 120 (2008) 1193
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174
d/d from Attractive + Repulsive Core a-a Potential
Arun K Jain & Bhushan N. Joshi, Prog. Theor. Phys. 120 (2008) 1193
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FR DWIA A2A CODE
0 ℓ (r, q, , R, Q, Φ ) 60 90, 64, 64, 22, 22, 22
1 ℓ m (r, q, , R, Q, Φ ) 60, 121 90, 64, 64, 22, 22, 222 ℓ m (R, Q, Φ) 60, 121 22, 22, 22Y(R) (R, Q, Φ)
22, 22, 22tℓ (r) ℓ (r, q, ) 60 90, 64, 64Dℓ m () ℓ m
60, 12164*64*90*22*22*22 3.9*109 Multiplications60*60*121*60*121*60*60*121= 1.38*1015 Sums
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(α, 2α) results
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Arun Jain & Bhushan Joshi
P R L, 103 (2009)132503140 MeV 16O(a, 2a)12C
Repulsive a-a potential explains the spectroscopic factor
90 MeV 16O(a, 2a)12CRepulsive a-a potential explains the spectroscopic factor
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Arun Jain & Bhushan Joshi
P R L, 103 (2009)132503
90 MeV 9Be(a, 2a)5HeRepulsive a-a potential explains the spectroscopic factor
197 MeV 9Be(a, 2a)5HeAttractive a-a potentialexplains the spectroscopic factor
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Arun Jain & Bhushan Joshi
P R L, 103 (2009)132503200 MeV 12C(a, 2a)8Be
Attractive a-a potential explains the spectroscopic factor
140 MeV 12C(a, 2a)8BeRepulsive a-a potential explains the spectroscopic factor
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Arun Jain & Bhushan Joshi, P R L, 103 (2009) 132503
Reaction Eα Sα(MeV) (R+A) (A) Theory
9Be(α,2α)5He
197 0.011 0.24 0.57
140 0.164 5.2312C(α,2α)8B
e200 0.02 0.7 0.55, 0.29
140 0.2 7.416O(α,2α)12C 140 0.55 20.6 0.23, 0.3
90 0.4 4.75
Comparison of (α, 2α) Spectroscopic factors from FR-DWIA calculations on 9Be, 12C, 16O nuclei at various energies
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Understanding:-In the shell model picture the two a’s can not physically overlapunless their nucleonic wave functions satisfy Pauli Principle.Which means that their shell model single particle orbitals are tobe occupied by the second set of 2-neutrons and 2-protons withtheir single particle 1s -1p energy gap. Which can be seen in the excitation of a -particle at ~20 MeV.4-particles of the other alpha to be promoted to this level requirean excitation of ~80 MeV.In the a - a lab system it will be ~160 MeV.Thus the two a’s repel each other below this lab energy.
Thus we have achieved an explanation of most of the puzzling
features of the Direct Nuclear Reactions.
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=Proton=Neuron
1S1/
2
Rαα
Eαα/4
α-α Repulsive Core + Attractive Potential
Eαα/4
1P3/2
1S1/2
Rαα=0
α-α Attractive PotentialExplanation of α-α potential in RGM - Shell Model picture
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Heavy Cluster Knockout
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(a, 2a)
(C, 2C)
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C C
CC
O α α
Comparison of 16O (a,2a) 12C and 16O (12C, 212C) 4He
16O(C,2C)a was performed at Mumbai LINAC-Pelletron at EC=119 MeV
α α
α
C CO
α
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Summed energy spectrum for the 16O(12C, 212C)4He Reaction Bhushan Joshi et al, P R L 106 (2011)
022501
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Comparison of Theory and Experiment: energy sharing distribution for 119 MeV 16O(C, 2C)4He Reaction:-
ZR-DWIA
FR-DWIA
Bhushan Joshi, Arun Jain, Y. K. Gupta,D. C. Biswas, A. SaxenaB. V. John, L. S. Danu,R. P. Vind and R. K. Choudhury P R L 106 (2011) 022501
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Proje- ctileEnergy (MeV)
Reaction Exptl. X-
Sectionb/sr2 MeV
ZR-DWIA X-
Sectionb/sr2 MeV
Sa ZR-
DWIA
FR-DWIA X-Section
b/sr2 MeV
Sa FR-DWIA
Theory
A R+A A R+A
140 16O(a,2a)12C 10.5 0.96 11 0.51 19.1 20.6 0.55 0.23
119 16O(C,2C)a 125±50 0.56 222 12.5 138 10 0.9 0.23
Comparison of the (a, 2a) and (C, 2C) reactions on 16O
Comparison of Sa (ZR-DWIA) indicates an enhancement of
20 times more in (C, 2C) case as compared to (a, 2a) case
A comparison of Sa (ZR-DWIA) with theory indicates an enhancement of 965 times in the (C, 2C) case
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BBLAABBaBaB
ifLfi
RdrdRrkrtRkrk
drrgkkT
212211)(
0121222)*(
2)*(
1 )(),()(),(),(
)(),(
a
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Summed Energy Spectrum of 24Mg(12C, 212C)12C at 104 MeV. Q=13.9 MeV at coplanar symmetric angle of 40.50
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Energy sharing spectra of 24Mg(12C, 212C)12C at 104 MeV with Q=13.9 MeV
at coplanar symmetric angle of 40.50
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Summed Energy Spectrum of 24Mg(12C, 212C)12C at 104 MeV. Q=13.9 MeV at coplanar symmetric angle of 36.70
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Summed Energy Spectrum of 24Mg(12C, 212C)12C at 104 MeV. Q=13.9 MeV at coplanar symmetric angle of 33.90
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• Finite Range with distortions explain elastic as well as knockout data.
• One can do heavy cluster knockout similar to (C,2C) reaction to study the short distance behaviour of the heavy clusters vertex (Repulsive core radius).
• The repulsion arises from the antisymmetrization of the many fermions system. • Distortions due to the residual nucleus can be used as an
observer (not just a spectator) of the knockout vertex.• Knockout reactions are very sensitive to the interaction at the
knockout vertex. Which has never been imagined by earlier workers.
• Heavy cluster knockout is possible to analyze because of our Finite Range Formalism and program.
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Shrinkage of Deuteron in 6Li
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Surface Clustering in Light Nuclei
q
R r
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q
R r
Surface Clustering in Light Nuclei
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q
R r
Surface Clustering in Light Nuclei
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q
R r
Surface Clustering in Light Nuclei
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q
R r
Surface Clustering in Light Nuclei
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q
R r
Surface Clustering in Light Nuclei
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q
R r
Surface Clustering in Light Nuclei
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q
R r
Surface Clustering in Light Nuclei
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q
R r
Surface Clustering in Light Nuclei
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q
R r
Surface Clustering in Light Nuclei
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q
R=0
Surface Clustering in Light Nuclei
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q
Rr
Surface Clustering in Light Nuclei
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q
Rr
Surface Clustering in Light Nuclei
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q
Rr
Surface Clustering in Light Nuclei
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q
Rr
Surface Clustering in Light Nuclei
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q
Rr
Surface Clustering in Light Nuclei
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q
Rr
Surface Clustering in Light Nuclei
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q
Rr
Surface Clustering in Light Nuclei
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0 20 40 60 80 20 40 60 80 θ0
CM Degree
4
3
2
1
Arb
Uni
t
dEddd
pt 3
Kα= 0 Kα= 30 MeV/c
Shift of the Angular distribution of Li6(d, tp)He4 reaction to larger angles for k α= 30 MeV/c exhibiting shrinkage of d - cluster in 6Li as it approaches α - cluster
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0 5 10 15 20 R(fm)
Sin
(kαR
)/(k
αR)
x R
2 ψdα
(R)
(Arb
. Uni
ts)
3
2
1
Kα= 0
Kα= 30 MeV/c
Plane wave overlap function for Li6(d, tp)He4 Reaction ~28 MeVPRL. 32 (1974) 173
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As seen in the previous figure, when the Deuteron cluster goes farther away from the a cluster (when Ka= 0 MeV/c) the transition amplitude has relatively more contribution from larger Rd-a.
Otherwise, corresponding to Ka= -30MeV/c the 6Li(d, t p)4He is expected to display more contribution from the distorted deuteron and if the n-p residual interaction in Deuteron cluster is long range type then we will see shrinkage.
It is clear from next slide; as compared to the free d(d, t)p distribution (free Deuteron cluster), the c.m. t-p angular distribution of the 6Li(d, t p)4He reaction shifts outwards. Which means that the relative momentum between the n – p of the deuteron cluster in 6Li increased.
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from Halo to !!! Hollow
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4He 4He
4He
R=0R=1-2 fm
R=4-6 fm
11Li 4He + 7H
Halo to Hollow !!
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OtherwiseDeflation of a balloon when the surface tension is larger that
the pressure inside the balloon. It nicely represent the decay of a cluster to a compact shape
when the long range N-N residual interaction is strong.
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Core Knockout Reaction of a Halo Nuclues:-
4He(11Li, 2α)7H at E0~ 300 MeV
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Core Knockout Reaction of a Halo Nuclues :-
4He(6He, 24He)2n
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Core Knockout Reaction of a Halo Nuclues :-
9Be(11Li, 9Li 9Be)2n
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Conclusions:-
1. In case of (a, 2a) knockout reactions there is a transition from 160 MeV to 200 MeV, where the a-a interaction changes from repulsive to attractive potential.
2 One can by explain the sudden change in reaction cross sections considering the strong interaction vertex.
3 One can do heavy cluster knockout similar to (C,2C) reaction to study the short distance behaviour of the heavy clusters vertex (Repulsive core radius).
4 Preliminary data analysis and understanding of the 24Mg(12C, 212C)12C Reactions at 104 MeV suggest that 24Mg(g.s) can not be described in terms of two Carbon-12 (g.s) clusters.
5 Data also indicated that 16O knockout from 24Mg is very significant leading to 24Mg as 16O+8Be
6 This also can be used to study the very weakly bound nuclei such as 11Li, 8He, 6He etc by core knockout reaction etc.
7 This way one can probably arrive at “HOLLOW” nuclei.
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235
In the present project we would like to study the heavy ion knockout on 28Si and 32S using 24Mg and 28Si Beams respectively at the Mumbai LINAC in order to compare these reactions with the corresponding (a,2a) reactions.
28Si(24Mg ,2 24Mg )4He vs 28Si(α , 2 α.) 24Mg 32S(28Si ,2 28Si )4He vs 32S(α , 2 α.) 28Si.
.This way we will be able to observe the influence of bigger and bigger knockout vertices on the knockout reactions.