Study of nucleon pairs in nuclei

Progress in Particle and Nuclear Physics PERGAMON

Progress in Particle and Nuclear Physics 44 (2000) 113- 122

_

http://www.elsevier.nl/locate/ppartnuclphys

Study of Nucleon Pairs in Nuclei P. Grabmayr

The study of nucleon pairs in nuclei with real and virtual photons aims towards an understanding

of the behaviour

of nucleons in nuclei at short relative distances.

Cross sections for the (-(,NN) and (e,e’NN) reactions on light nuclei have been measured at the Main% electron accelerator

MAMI in search for nucleon-nucleon

lations and as basis for tests of respective model calculations. mechanisms

as meson exchange and isobaric currents

tion must be separated. as signatures

on high energy resolution pin down the respective

1

as well as final state interac-

The observed high momentum

of the nucleon-nucleon

correlations.

corre-

Effects of competing

components

are interpreted

Future experiments

to resolve final states - a constraint

concentrate

which will help to

reaction amplitudes.

Introduction

Right from the beginning

of the nuclear shell model the behaviour

within the nuclear medium has been under discussion. the nucleon-nucleon

(NN) potential

approx.

0,5 fm was not understood.

distance

is particularly

In contrast

short compared

reactions

of high resolution

at short relative

shell model

orbitals

example,

without

the occupancy

Fig. 2. The initially

to the diameter

of nucleons

low energy properties

variational

distances. pointing

directly

of the 351,~ orbitals

calculations

of one-nucleon

due to NN correlations

is shifted towards

the one nucleon-removal

experiments

reactions.

(1, 21 can only measure

the occupancy

the doubly

shift of strength.

magic “‘Pb

energies and cannot

of As

is shown in

completely

It was shown by H. Miither

full shell

that the strength

be observed

correlations

had been suggested

directly

in

Both probes are understood

already in the 50-ies, as e.g.

to be absorbed

dominantly

- see front matter 0 2000 Published by Elsevier Science BV All rights reserved. PII: SO146-6410(00)00064-8

0146-6410/00/$

and knockout

of nucleon-nucleon

in nuclei around

high excitation

the new

feeding low lying states.

for access towards

pion and photon induced

below

revived the discussion

at the origin of the observed

the same amount.

somewhat,

transfer

empty shell in ‘04Hg is filled by about 25% while the initially by roughly

in

(cf. Fig. 1). While the success of

silenced the criticism

investigations

These experiments

in 206,20aPb is depleted

Other methods

of the very strong repulsion

to the atomic case for nuclei the average inter-nucleon

and high precision

as well as the accompanying

correlations

The smoothening

at short distances

into an overall mean field which occurs at relative distances

the mean field models when describing generation

of two nucleons

on nucleon

114

I? Grabmayr / Prog. Part. Nucl. Phys. 44 (2000) 113-122

pairs at relative

tions, as e.g. the notorious

Figure

[3]. H owever, beam quality, energy resolution

close proximity

final-state

interaction,

prevented

serious progress.

and background

reac-

Thus, one of the strongest

1: Size and average relative

distance

of nucleons

Figure 2: Occupation

in nuclei.

probability

of the

3s1/2 orbit in Hg, Tl and Pb isotopes. argument nuclear

for short ranged effects in the nuclear medium binding.

for binding

A recent

of nuclear

ple Hartree-Fock NN potentials

by H. Miither

at the empirical yield binding

the same binding

different

off-shell behaviour

tering with equal quality. correlations

1: Energy

per nucleon

[4] are displayed

imation

EHF and compared

contributions

for three NN potentials

EHF

E Corr VTHF Vlrcorr

detectors

a renewed approach

is poorly defined,

obtained

NN correlations.

This clearly

however tensor

type

[4]. saturation

in the Hartree-Fock

calculations

CDB

ArgV18

4.64

30.34

12.08

-17.11

-15.85

-15.82

16.7

15.8

15.0

-40.35

-28.98

-2.30

of experimental

modern

(Ecmr).

density.

approxDifferent

(VnHF) and

( VrCorr) are found for the three potentials.

techniques

on one side and new developments towards

have been found.

to the total energy in Born approximation

MeV/A

Sim-

from Brueckner-Hartee-Fock

at the empirical

to Brueckner-Hartee-Fock

the effects of correlations

However, the new generation

matter

of

which fit the phase shifts for NN scat-

for the rzp channel

for nuclear

NN potentials.

While for different

is extracted

of the n exchange

part of these potentials

of the n exchange

those including

point using realistic

of these three potentials

investigations

the need of NN correlations

only with effective potentials.

contributions

The tensor

Results

resolution

saturation

play a crucial part in the calculations

Table

[4] demonstrates

energy per nucleon

(Ec0t.r in Tab. 1) different

calculations indicates

matter

calculation about

compilation

still arises from theoretical

Nijml

for cw accelerators

of nuclear structure

and large area, high

and reaction

models permit

There are several kinds of trivial correlations

as e.g. due

115

I? Grabmayr /Prog. Part. Nucl. Phys. 44 (2000) 113-122

to Pauli principle density

or conservation

of centre-of-momentum

in the “free” two-nucleon

PNN:

The dynamical connected

free C+

correlations

e.g.Pauli-correlations

are in the centre

with short inter-nucleon

r2!

=

approaches

are obtained

from the two-hole

[4, 5, 121 and the deviation

correlation

function.

PNN

diagrams

contrasted

by the Valencia

model

functions,

approximation

to apply the nuclear matter

correct

observables

momentum

the difference

between

momentum

is expressed

photon

of restricted

photon

of kinetic energies of particles

Note, that nal state.

calculate

these three

of the pair.

momentum

are

completely

energy,

while the former models

the missing

The missing

(PWIA)

final states.

momentum

momentum

and the

P; is defined

nucleon momenta p,

to the

6” and &:

can be interpreted

This governs the gross features

as

as the

of the angular

and

The missing energy E, = k - T, - Tp - TR is defined as the in the incoming and outgoing reaction

observables

are defined

relativistically

only in PWIA

to get a handle

model assumptions

channels.

In particular,

from p,.

Finally, the

about

and are relevant

of the relative

the binding

only in the fi-

momentum

and the photon

coupling

p’, in the one can

9;. calculations

the competing

or in general

specific quantum

numbers

[6,7] permit a proper treatment

of the two-nucleon

knockout reaction

Effects

of the NN correlations

are expected

components

in angular distributions

different from the quasideuteron

processes.

through excess of high momentum prediction

and the most

mechanisms

mechanisms

i and the outgoing

approximation

there is no possibility

Only through

State-of-the-art including

emission

is defined as P; = i(&, - fl,,).

In particular,

initial state.

or

The above models

absorption

TR is the kinetic energy of the recoiling (A - 2) system calculated relative momentum

the two-nucleon

ranges of low missing energy or selected

are the missing

In plane wave impulse

of the cross sections.

function

result to real nuclei. The latter model, after tailoring

the two nucleons

incoming

as defect

absorption.

all photon

by various

however, it uses a Fermi gas model and local density

P of the pair before the interaction.

energy dependence difference

treatment;

of importance

between

= i - & - &

which are calculated

as possible the nuclear structure

is used for studies of the reaction

are used for the direct comparison

relative

as complete

[13] which includes

mechanically

The three

(2)

spectral

of real or virtual

by a quantum

situation,

those which can be

fiN

X

The latter serve as input to models [6, 71 which calculate

(see Fig. 4, bottom)

actual experimental

-

to the mean field result

process to specific final states by including dominant

and in particular

geZe

dynamic These densities

of interest

distances Cdyn(T1,

p;

which are included

in unexpected

variation

can be selected.

of cross sections,

particular

to be recognised

when final states

with

116

I! Grabmayr /Prog. Part. Nucl. Phys. 44 (2000) 113-122

Experiments

2

Figure 3: Experimental ger, proton

hodoscope

tron time-of-flight matical

The experiments

of the PiP/TOF

Mainz using the Glasgow tagging thin Ni radiator

group are performed

spectrometer

or on 100 pm thick diamond

PiP [14] and neu-

array [15]. Three kine-

regions are indicated.

at the cw electron

[16]. Electron

beams

crystal in case polarised

photons

electron

momentum

which have been slowed down during the bremsstrahlungs

beam is collimated which consist photon

in order to be well defined

either

of liquid helium

flux is calibrated

efficiency’

to free running

measurements,

at reduced

intensity.

whereby

Typical

a ring of 1 mm thick plastic detectors

for neutrons

layered hodoscope

The energy

correction

for quenching

the time-of-flight in TOF

counters,

Protons

Charged

particles

are discriminated

against

deuterons

exclusively

by TOF with an average FWHM

by appropriate

cuts on pulse height

of graphite

(E,,,)

direction

targets

or lithium.

is surrounded

particles

are detected

beam by

and as veto

by the fivefold

and pions via the AE - E

from the pulse height

after proper

energy is obtained

vs. time-of-flight.

Beyond

of 6 MeV has been obtained. into a momentum

from

particles

radioactive

is the best means of calibration

can be translated

The

‘tagging

is setup in the photon The target

the

The photon

of about 0.7 ns. The charged

of the deuteron

An overall energy resolution

process.

for charged

from TOF[15].

is extracted

The dipole

focal plane by so-called

have been obtained.

which act as start detectors

of 3 ’ in polar and of 9 ’ in azimuthal

of 35 MeV/c.

the tagger

are needed.

on 4 pm

1,5 cm) on the nuclear

can or of sheets

scalers within

sources and cosmic rays the photodisintegration

resolution

of approx.

MAMI at

the hall and it analyses

and energy losses in air and dead layers. The neutron

measured

system.

a kapton

values of ~=45f2%

of these particles

can be selected

the complete

(diameter

outside

a 100% efficient lead glass detector

to be selected

PiP[14].

technique.

within

cup located

accelerator

of 855 MeV impinge

bends the undisturbed of electrons

beam into a Faraday

setup with tag-

for

The angular resolution

l? Grabmayr / Prog. Part. Nucl. Phys. 44 (2000) 113-122

I11

Reaction mechanisms

3

An overall picture

of the competing

of the data to the predictions energy spectra

For 4He a qualitative

energies

at higher

the yield at low E,

photon

energies

(x150

- Q of the residual

It is observed

photon

relative

that even at highest

absorption

to that

by

process.

for “C

The yield

due the reduced

on low excitation

energies

Bottom:

for photon

absorption

Contributing

reaction

on “C and 4He compared mechanism

to pre-

for 2N absorption,

pion

and 3N absorption.

E.,=(135+20)

observed.

can be stated.

arises from the two-body

cross sections

Next, we focus on the angular

is covered

agreement

energy bins the missing

The “C data are well described

These findings permit the concentration

with the Valencia model.

production

model 1131. For three photon

on “C and 4He are plotted.

[17, 18, 91

best by comparison

nuclei.

Figure 4: Top: experimental dictions

is obtained

MeV) for 4He is reduced

influence of final state interactions. E, = E,

mechanisms

of the Valencia

for the (y,np) reaction

the calculations. photon

reaction

MeV [19]. With

(see Fig. 5, left).

three detector

The dominant

settings

as indicated

indicates

the acceptance-integrated

with (without)

by the small white rectangles

considering

experimental

Fermi motion

MeV and at

a very large part of the relevant

phase space

back-to-back

In order to obtain the angular distribution

summed

<50

of the i2C(y,np)

distribution

reaction

emission

at E,

of neutron

and proton

is clearly

shown in the right of Fig. 5 the counts have been along the ridge.

The thin solid (dot-dashed)

cross section for photodesintegration

of the np pair within

the carbon

nucleus.

line

of the deuteron The failure to

P Grabmayr / Prog. Part. Nucl. Phys. 44 (2000) 113-122

Figure 5: Angular

distribution

of the 12C(y,np) reaction

describe the data is a clear indication processes

beyond

exchange

currents

of medium modification

the simple quasideuteron can account

at E, ~50 MeV and at E,=(135+20)

picture.

Proper

for shape and magnitude

0 0.5

....’ -.-.-

of the pair and of existence calculations

[7] including

MeV.

of additional

X- and p meson

of the data.

2N knockout phase space total

--

Valencia model 2N Valencia model PN+FSI

0 0

500

1000

Recoil Momentum (MeVk) Figure 6: Recoil (missing)

The compilation

momentum

(Fig. 6) of recoil momentum

distributions

distributions

for a large photon energy range from 150 to 700 MeV demonstrated can be described the Valencia

very well by a two-nucleon

model can explain

Only at high momenta

beyond

for the three kinematical impressively

model baaed on the Gottfried

the data reasonable 500 MeV/c

from ref. [8]

deviations

well despite

and

that these distributions

approximation

their large variation

can be found.

settings

[3]. Similarly of magnitude.

For an unified comparison

the

Part. Nucl. Pbys. 44 (2000) 113-122

P Grabmuyr/Prog

data from the various kinematics

are divided by the respective

the excess of high momentum

components

alternative

wave functions

use of uncorrelated

explain the increase, tensor correlations recoil momentum

however,

is evidently

a prediction

of Saxon-Woods

[12] reproduces

due to nucleon-nucleon

within the (A - 2) residual

one which is remaining

data sample it will be important

0

100

recoil momentum

200

300

energy range 300< E7 <400 MeV normalised

4

and dotted

wave functions

the trend correctly.

nucleus.

400 500 P, (hw//c)

in LOA including

The increase

at high

involving one ejected nucleon and

distribution

700

in this broad

for individual

states.

600

from the 3 choices of kinematics

by the prediction

The

lines) cannot

As FSI can not be excluded

600

In Fig. 7

of the choice of kinematics.

correlations

distributions

of the 2N model.

type (dashed

to show the recoil momentum

‘* 11

Figure 7: Experimental

independent

(solid line) of correlated

by Sarra and Orlandini can explained

predictions

119

in the photon

of the 2N model from ref. [S].

High resolution two-nucleon emission experiments

Despite

the new insights

ageing over all states as ambiguities solved.

obtained

with the experiments

we presently

to nuclear structure

aim for two-nucleon

In general only a few partial waves contribute are predicted

above, it turned

of a single shell model orbital does not pin down the reaction

of the model with respect

Therefore,

described

to exhibit

distinctive

emission

to a transition

distributions

depending

or reaction experiments

out that the avermodels sufficiently

amplitude

may not be re-

which resolve final states.

to a single final state.

The cross sections

on the spin and isospin quantum

numbers

of the final states. The nucleus perimental

“0

is the best candidate

and from theoretical

for short range correlations vestigated

when searching

considerations.

from the nuclear

structure

High resolution

of scalar type are reported for the tensor type correlations

elsewhere

point of view both from ex-

(e,e’pp) experiments [lo].

and the search

The np channel

as they are not present

must be in-

in the pp channel.

P Grabmayr/ Prog. Parr. Nucl. Phys. 44 (2000) 113-122

120

Figure 8: Predicted the 160(e,e’np)14N

momentum reaction

distributions

to NN correlations

Fig. 8 correspond dominant the partial distributions.

waves.

as predicted

The different

Table 2: Properties

to measured

in the shapes

of the four sets in

are explained

of the missing

of fractional

parentage

L

cfp

$

0.0

1+,0

(P1/2)-2

2

0.21

1.4f

2.3

O+,l

(PI/z)-”

0

-0.19

-

3.95

l+,O

(fJl,2)-1(p3/2)-1

0

-0.19

1.7 & 0.5

7.03

2+,O

(.~1/2)-~(~3/2)-*

2

0.28

1.6f

11.05

3+,0

2

0.33

-

(P3/2)-2

results from a low energy high resolution in Lund.

Unfortunately,

Despite the same coefficient

(cfp)

of the sensitivity of fractional

[$I 0.5

0.4

160(Y,np)‘4N

no missing

in order to verify the angular

give a nice example

momentum

[20].

configuration

cross sections

and thus

on 3He and 160 are in preparation.

J;I, T

in this experiment

by the

lines) can make up to 50% of the cross sections;

in 14N. Coefficients

states

cross sections

at ET=72 MeV at MAXlab

nuclear structure.

are reflected

(Fig. 8, dashed

of low-lying

Table 2 and Fig. 9 present

the obtained

[7]. The final states

of Table 2. The spins of the states

First (e,e’np) experiments

E,/MeV

could be extracted

in

in the np channel there is a very specific

by J. Ryckebusch

contributions

The NN correlations

are compared

currents

of pr,s and ps/s removal; which in turn fixes the angular momentum

they affect also the shapes.

performed

of meson exchange

to the first four states

configurations

for the four lowest states

[7].

Despite the strong contributions sensitivity

and nucleon polarisations

momentum

momentum

transfer.

of the photoabsorption

parentage

experiment

predicted

[20]

distribution However, processes

to

by simple shell model

P Grabmayr / Prog. Part. Nucl. Phys. 44 (2000) 113-l 22

arguments

the cross section

has isospin

T=l

assumption

of observing

for the first excited

and is the isobaric all strength

analogue

121

state is less than 5% of its neighbours.

state

to the ground

for removal of p-shell nucleons

states

This state

of 14C and i40. With

the

one can derive an upper limit of

2% isospin mixing.

In preparation investigated

Figure 9: High resolution

‘60(y,np)‘4N

of the new high resolution

experiments

in order to complement,

of real and virtual Employing

photoabsorption

solid state

HP-Ge

clearly showed the feasibility. E, x6 MeV; as the resolution

reaction

will be

with the (e,e’pp) data of ref. [lo], the fourfold data set from 160 for a combined

with large solid angles and thickness

In Fig. 10 the ground

state transition

of the excited states is expected

analysis.

a pilot run of 5 hours

is well separated

is mainly governed by the tagger resolution

excitation

from levels at

which will be improved

by a

in future (y,pp) experiments.

energy / MeV

Figure 10: 5 hour pilot run for the high resolution

5

[20]

also the 160(y,pp)‘4C

each with pp and np emission

detectors

also a separation

“tagger microscope”,

together

experiment

160(y,pp)14C

experiment

[ll]

Summary

The present

status

high resolution

in search of NN correlations

experiments

in nuclei has been reported.

on 160 with real and virtual

photons

will permit

The new generation a stringent

state-by-

of

122

I? Grabmayr / Prog. Part. Nucl. Phys. 44 (2000) 113-122

state comparison

of measured

that the correlation in-medium

functions

properties

momentum

distributions

from different

with various model calculations.

potentials

can be selected

It is expected

and an understanding

of the

of nucleon pairs will be gained.

Acknowledgement I would like to acknowledge to all members

many useful discussions

of the PiP/TOF

with J. Ryckebusch

group for the great support

and H. Miither.

of our common

I am indebted

interest.

References [l] P. Grabmayr, [2] P.K.A.

Prog. Part. Nucl. Physics

de Witt Huberts,

[3] K. Gottfried,

29 (1992) 251

J. Phys. G, Nucl. Part. Phys 16 (1990) 507

Nucl. Phys. 5 (1958) 557

Induced [4] H. Miither, Proc. 4l”Workshop on “Electromagnetically Granada, May 26-29,1999; eds. P. Grabmayr and A. Lallena; p. 1 [5] W. Dickhoff,

ibid, p. 226; A. Fabroccini,

ibid, p. 206

ibid, p. 148; Nucl. Phys. A571

[6] C. Giusti,

et al., ibid, p. 182; D. Watts

[8] D. Watts

(1994) 694

ibid, p. 19; Phys. Lett. B383

[7] J. Ryckebusch,

Emisssion" ,

Two-Hadron

(1996) 1; private comm.

et al., submitted

to Phys. Rev.

[9] T. Hehl, et al., ibid, p. 70 [lo] G. Rosner et al. ; W.A.H. Hesselink

et al. contrib.

[ll] P. Grabmayr

et al., ibid, p. 331

[12] G. Orlandini

and R. Sarra, 2 nd Workshop,

[13] R.C. Carrasco

et al., Nucl. Phys.

(141 1.J.D. MacGregor [15] P. Grabmayr [16] I. Anthony [17] T. Lamparter

et al., Nucl. Instr.

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I201 L. Isaksson [21] J.Ryckebusch

et. al., Phys.

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A402 A301

(1996) 479

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(1996) 1

and clustering

Yau et al., Eur. Phys. J. Al

Erice, 1999

Gent, May 1997, p. 1

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to Int. School on Nuclear Physics,

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in subatomic

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Nucl. Phys. A 624 (1997) 581; private communication

physics”,

ed. O.Scholten,