Prakash Chandra Rout

Nuclear Physics Division

Bhabha Atomic Research Centre

Shell effect studies in level density

� Introduction

�Motivation

�Experimental details

�Data reduction and results

�Summary

Outline of the talk

Introduction:

Shell effect is a cornerstone of the mean field theory describing finite

fermionic systems

Filled proton and neutron shells with magic configuration gives an

extra stability with respect to that expected from the average

behaviour described by the liquid drop model

Physical phenomena influenced by shell effect • Fission isomers

• Super heavy elements

• Super-deformed nuclei

• New magic numbers in exotic nuclei

Shell effect also affect the nuclear level density

(a)Resonance spectra of slow neutrons

(b) Direct count of levels populated in charged particle reactions

such as (p, p'), (α,p), and so on

(c) Analysis of evaporation spectra

Main sources of evidence on NLD:

‘a’ increases linearly with the mass

number of the nucleus (~A/8.5 MeV-1),

there is a large departure from this

behaviour at shell closures.

a ~A/26 MeV-1 at A~208

Shell correction in level density

Measurement of damping of shell effect near doubly closed shell

nucleus 208Pb

Motivation

Long standing prediction ……….

Shell effect on the NLD parameter is expected to decrease

asymptotically to its liquid drop value at Ex >40 MeV

V. S. Ramamurthy, S. S. Kapoor, and S. K. Kataria PRL 25 (1970) 386

No direct experimental measurement, spanning a wide EX range,

has been ever reported on this very important subject

One way is to measure evaporation particle spectra populating

low excitation energies in residual nuclei in this heavy mass region

Shell effect on nuclear level density as a function of EX is expected

to be pronounced near the doubly shell-closed 208Pb

There is a difficulty

So, populating low EX in residual nuclei after particle evaporation

is practically impossible

EX in parent Compound Nucleus is too high because of

the Coulomb barrier in the entrance channel

Measured proton evaporation spectra in 10;11B+198Pt reactions and

extracted the NLD in 208Pb at an excitation energy ~ 50 MeV

Washing out of shell effect

M. Lunardon et al., Eur. Phys. J. A 13, 419 (2002).

One possible way is

The measurement of particle spectra following the

transfer reaction populating low EX in the intermediate parent

nucleus

Measurement of continuum γ-ray spectra following inelastic

scattering and transfer reactions.

3He induced inelastic scattering and single nucleon transfer reaction

to populate 205-208Pb and extracted the energy dependence of NLD

from the coincident spectrum up to EX ~ 6 MeV

E. Melby et al., PRL 83, 3150 (1999)

N. U. H. Syed et al., PRC 79, 024316 (2009)

Effect of shell correction on ‘a’ can be seen by comparing the

particle spectra in the nuclei both near and away from shell closure.

Triton transfer fusion reaction on 205Tl and 181Ta to populate the CN 208Pb and 184W respectively and measure evaporation neutrons

Reaction: 205Tl(7Li, α)208Pb* → n+207Pb*181Ta(7Li, α)184W* → n+183W*

Beam:

30 MeV 7Li (pulse width ~1.5 ns, pulse period ~ 107 ns)

Targets:205Tl (enriched >98%) and thickness 4.7 mg/cm2

natTa and thickness 3.7 mg/cm2, 12C , Ta2O5

Detectors: α α α α : 8 CsI(Tl) - 2.5×2.5×1 cm3 coupled to Si(PIN)

θlab ~ 126 – 155o

Neutron: Neutron detector array(15 bars , 1m × 6cm × 6cm)

D~ 1 m , θmean ~ 90o

Energy from TOF

Experimental Details

CsI array

Neutron detector array

Shadow

pyramid

Experimental set up205Tl(7Li,αααα)208Pb* →→→→ n+207Pb*

181Ta(7Li,αααα)184W* →→→→ n+183W*

� TOF = 0.5* (TL+ TR ) + offset

� Position α (TL- TR )

� Q = √ (QL* QR)

� Multiplicity (Mn=1)

� Energy and PSD of CsI(Tl) detector

Data reduction:

Neutron energy (MeV)

2 3 4 5 6 7 8 9

dσ

/dE

(ar

b.

unit

s)

10-4

10-3

10-2

10-1

100 Ι

ΙΙ

ΙΙΙ

Time (ns)

140 160 180 200 220 240

Co

un

ts

1

10

100

1000

n γ

En = 2.0 MeV 9.0 MeV

Measured neutron energy spectra

Ex= 22.7 MeV

20.8 MeV

18.9 MeV

Statistical Model Analysis

Statistical model (SM) analysis of the spectra was done using

CASCADE with the EX and J dependent NLD

dσ

/dE

(ar

b.

un

its)

10-4

10-3

10-2

10-1

100

101 data 205

Tl

∆S=2.2 MeV

∆S=13.1 MeV

Neutron energy (MeV)

2 3 4 5 6 7 8 910-5

10-4

10-3

10-2

10-1

100

101 data 181

Ta

∆S=2.2 MeV

∆S=13.1 MeV

Statistical Model Analysis

Statistical model (SM) calculation

ã = A/8.5 MeV-1

γ = 0.055 MeV-1

σα= 40 mb

shell correction energy ∆s = 13.1 MeV

( for 207Pb) fits the shape of neutron

spectrum for the Tl target while ∆s =2.2

MeV does not

Ex= 20.8 MeV

Ex= 20.6 MeV

Excitation energy dependence of the NLD parameter (Ignatyuk-1975)

Constraining all three parameters ( ã, ∆S and γ) is not possible from the data

addressing even a much wider excitation energy range.

Since the shell correction energy is known with a reasonably good accuracy

(within a few hundred keV )

Fixed ∆S and searched for an acceptable range of ã and γ

Shell correction energy for 207Pb and 206Pb are 13.1 and 11.7 MeV , respectively

dσ

/dE

(ar

b. u

nit

s)

10-4

10-3

10-2

10-1

100data

205Tl

γ = 0.035 MeV -1

γ = 0.060 MeV -1

γ = 0.075 MeV -1

Neutron energy (MeV)

2 3 4 5 6 7 8 9

1

2

3γ = 0.035 MeV-1

γ = 0.060 MeV-1

γ = 0.075 MeV-1

(a)

Rat

io

(b)

Extraction of damping parameter

A change in the ∆S value to 0.5 MeV

has <2% effect on the shape of the spectra

Statistical model fits for the central bin

for ã= A/8.5 MeV-1 and three γ values.

γ = 0.060 MeV-1 gives a good fit

δa (MeV)

7.5 8.0 8.5 9.0 9.5 10.0

γ (

MeV

-1 )

0.02

0.04

0.06

0.08

Allowed values of δδδδa & γ ?γ ?γ ?γ ?

Neutron resonance data,

γ= (0.079 ± 0.007) MeV-1

Mughabghab & Dunford

PRL 81 (1998) 4083

Statistical model calculation for all three energy bins:

δa (= A/ã) = 6.5 - 11.0 MeV & γ = 0.02 - 0.08 MeV-1

arXiv 1210:3213 [nucl-ex], accepted in PRL

Shell damping factor:

� Large shell correction (13.1 MeV for 207Pb and 11.7 MeV for 206Pb)

is required to explain the neutron spectra from 208Pb*

�An exclusion plot on level density parameter and damping factor

has been made

�Shell damping factor extracted from the present data

Summary

Possible improvement :

� For Charged particles Si CD or Strip detector

Response is linear

measure simultaneously all light charged particle

(handle on various reaction channels)

� Using liquid scintillator (LS) detectors ( ~ efficiency )

Pulse shape discrimination & TOF

(no ambiguity in n-γ discrimination)

Angular distribution

( contribution of non-compound nuclear component)

� Improvement of beam timing (sharper beam profile)

Collaborators:

D. R. Chakrabarty

V. M. Datar

Suresh Kumar

E. T. Mirgule

A. Mitra

V. Nanal

S. P. Behera

R. Kujur

Vivek Singh

(BARC-TIFR)

Acknowledgement:

S. S. KapoorNitali Dash

A. B. Parui

M. Pose &

Pelletron staff

Thank you for your kind attention

Energy dependent threshold Eth (En)E

th (

keV

)

En (MeV)

205Tlt

α7Li

Time (ns)

260 280 300 320 340 360 380 400 420

Co

un

ts /

0.5

ns

100

101

102

103

104

105

n

γ

γR