Nucleon-nucleon correlations inside atomic nuclei synergies observations and theoretical models Ranjeet Dalal1 and I.J. Douglas MacGregor2

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Nucleon-nucleon correlations inside atomic nuclei:

synergies, observations and theoretical models

Ranjeet Dalal1, and I.J. Douglas MacGregor2

1Guru Jambheshwar University of Science and technology, Hisar, India

2SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ,

United Kingdom

E-mail: ranjeet@gjust.org

August 2022

Abstract. While the main features of atomic nuclei are well described by nuclear

mean-ﬁeld models, there is a large and growing body of evidence which indicates an

important additional role played by spatially-correlated nucleon-nucleon structures.

The role of nucleonic structures was ﬁrst suggested by Heidmann in 1950 to explain

pick-up reactions of energetic nucleons. Since then a steady ﬂux of new experimental

evidence has conﬁrmed the presence of similar structures inside atomic nuclei,

dominated by correlations between pairs of nucleons. The role of these internal

nucleon-nucleon correlations has been established using various energetic probes like

photons, pions, leptons and hadrons. These correlated structures are essential for

understanding the interaction of particles with nuclei and their presence provides

an explanation of many speciﬁc nuclear phenomena including backscattered protons,

copious deuteron production, sub-threshold particle production, neutrino interactions

with nuclei and the EMC eﬀect. On the theoretical side, these measurements have

stimulated a large number of phenomenological models speciﬁcally devised to address

these enigmatic observations. While reviews exist for speciﬁc interactions, there is

currently no published commentary which systematically encompasses the wide range

of experimental signatures and theoretical frameworks developed thus far. The present

review draws together the synergies between a wide range of diﬀerent experimental and

theoretical studies, summarises progress in this area and highlights outstanding issues

for further study.

arXiv:2210.06114v1 [nucl-th] 12 Oct 2022

Nucleon-Nucleon correlations inside atomic nuclei 2

1. Introduction

The internal structure of nuclei has traditionally been investigated using a wide range

of energetic probes, leading to the ejection of one or more nucleons, or to meson pro-

duction. These probes include photons [1], pions [2], electrons [3], protons [4], neutrons

[5] and neutrinos [6]. The interaction of probes with nuclei have provided vital infor-

mation about the state of the nucleus and individual nucleons just before the interaction.

The interaction of energetic photons with nuclei was initially expected to result in

the ejection of individual nucleons [7] from speciﬁc shell model orbits. However, the

observed nucleon angular distributions, cross-sections and the ratio of ejected protons

and neutrons measured in early experimental work, led Levinger [8] to conclude that

in many cases more than one nucleon was involved in the interaction. To explain these

unexpected observations, he formulated the simple quasi-deuteron model (QDM) in

which neutrons and protons often occur in deuteron-like structures inside nuclei. The

resulting model, which is at odds with the nuclear shell model, has been quite successful

in explaining the various subtleties of photon interactions with nuclei for Eγabove 40

MeV [9, 10, 11, 12, 13, 14]. In this quasi-deuteron process, the photon-energy absorp-

tion predominantly takes place on a strongly interacting neutron-proton pair while the

remaining nucleons act as spectators, making the (γ, np) reaction an attractive tool to

investigate 2N correlations in nuclei.

The dominance of quasi-deuterons, or spatially correlated neutron-proton struc-

tures inside nuclei, was also conﬁrmed by measurements of charged-pion absorption in

nuclei [2], where absorption on two-nucleon pairs has undergone extensive testing since

the 1950s.

Note that the nature of the correlation, or interaction, between the interacting

nucleons depends on their spatial separation. At long range it is often modelled by

single-pion exchange mechanisms, while at shorter distances it may involve multiple

meson exchange or direct quark or gluon exchanges, if the nucleons are close enough

to overlap. In general, higher energy probes are required to study shorter spatial sep-

arations and the commonly used term Short Range Correlations (SRC) is reserved for

correlations studied with such high energy probes.

Recently, the inclusive and exclusive quasi-elastic reactions (p, p0NN) and (e, e0NN)

have been investigated at very high momentum transfer at BNL [4] and Jeﬀerson Lab

[3], respectively, where the angular correlations between ejected nucleons have been

studied to reveal the state of nucleons just prior to the interaction of energetic probe

particles. For ejected nucleons with momenta above 250 MeV/c, it has been observed

[4] that around 92% of the time protons ejected from 12C targets are accompanied by

correlated neutrons. The most likely explanation is that the emitted high-momentum

Nucleon-Nucleon correlations inside atomic nuclei 3

nucleons originate from short-range spatially correlated nucleon pairs. Such SRCs in-

volving neutrons and protons are similar in construct to the quasi-deuteron concept ﬁrst

formulated to describe lower energy interactions.

The presence of a signiﬁcant fraction of nucleons in strongly correlated 2N clusters,

mainly quasi-deuterons or neutron-proton SRCs, leads to many other subtle observations

including enhanced deuteron ejection by energetic probes. Pion absorption reactions [2]

have led to copious deuteron ejection (up to 25% compared to the yield of ejected pro-

tons or neutrons) from nuclei. Similar observations were reported by Baba et al. in

1984 for photons of multi-hundred MeV energies [15]. A signiﬁcant fraction of energetic

photon and pion absorption events result in either the predominant and simultaneous

ejection of kinematically correlated proton-neutron pairs, or the emission of deuterons.

The presence of nucleon-nucleon correlations inside nuclei was ﬁrst used to explain

the properties of pickup reactions by energetic neutrons [16]. A notable example is

copious deuteron ejection observed at forward angles by multi-hundred MeV hadrons,

reported in early experiments by Azhgirei et al. [17]. This was understood in terms

of underlying quasi-deuteron degrees of freedom inside nuclei by Sutter et al. [18].

These observations have been conﬁrmed by recent experiments where the coincidence

measurement of elastically scattered protons and deuterons are used to investigate the

spin-isospin character of SRCs at Osaka [19]. The unexpectedly high deuteron pro-

duction, observed in numerous experiments using collisions of multi-GeV relativistic

protons (for example, the early work of Cocconi et al. [20]), may be seen as extension

of Azhgirei and Sutter’s quasi-deuteron propositions.

There have been many other independent manifestations of few-nucleon quasi-

bodies inside nuclei, for example neutrino interactions with nuclei [6, 21], including the

signiﬁcant fraction of 2-proton emission events [22], the observation of backscattered

protons with unexpectedly high energy for multi-hundred MeV proton beam [23, 24],

the sub-threshold production of particles [25, 26] and the EMC eﬀect [27].

On the theoretical side, there have been intense activities to explain unexpected ob-

servations, most notably the development of the independent pair model or IPAM [28]

and through the high-momentum components of nucleons in an independent particle

framework [3]. The other notable models considering SRCs inside nuclei are the unitary

correlation operator method (UCOM) [29] and recently proposed contact formalism [30].

The present work is an eﬀort to encompass a wide range of experimental investigations

and theoretical works illuminating the correlated structures observed within nuclei. A

holistic review may stimulate further investigations of these phenomena.

Nucleon-Nucleon correlations inside atomic nuclei 4

2. Experimental Indicators

The ﬁrst evidence for nucleon-nucleon correlated structures inside nuclei appeared

shortly after the availability of energetic beams of photons, neutrons and pions more than

70 years ago. The range of evidence supporting spatially-correlated nucleonic structures

has grown considerably since then. In this section, some of the key experimental

indicators of strong nucleon-nucleon correlations are discussed. Our intention is not

to present an exhaustive review of all the available evidence, but to underscore the

ubiquitousness of correlations observed through a wide and diverse set of experiments.

The most important observations advocating correlated degrees of freedom are:

(i) Interaction of energetic photons with nuclei through the quasi-deuteron mechanism;

(ii) Inclusive and exclusive reactions (e/p, e0/p0NN) using energetic electrons/ protons;

(iii) Pion absorption reactions where absorption of pions takes place mainly through

2N-absorption mechanisms;

(iv) Direct quasi-elastic knockout of deuterons at forward angles using nucleons of a few

hundred MeV energy;

(v) Backscattering of hadrons of several hundred MeV energy from nuclei and sub-

threshold production of energetic particles;

(vi) Interaction of neutrinos with nuclei;

(vii) The EMC eﬀect.

A schematic illustration of these interactions is shown in ﬁgures 1 and 2.

2.1. Interaction of energetic photons (Eγ>40 MeV) with nuclei

In photoemission reactions, the outgoing nucleons were expected to follow either the di-

rect photoelectric process developed by Courant [7] in which photon energy is absorbed

by individual proton leading to its ejection from nucleus, or the statistical theory of

Blatt and Weisskopf [31] in which nucleons are assumed to “boil oﬀ” from the excited

compound system. However, it rapidly became apparent that the photo-neutron and

photo-proton production cross sections, and their ratio, could not be accounted for by ei-

ther of these reaction models. It became possible to investigate the photo-disintegration

of nuclei with much higher photon energies with the advent of bremsstrahlung photons

from synchrotrons. It was expected that only nucleonic degrees of freedom would be

important for Eγ∼100 MeV, and the (γ, p) reaction would be much more probable due

to its strong electric dipole component. In comparison the (γ, n) reaction has a much

weaker magnetic dipole contribution. Furthermore, no signiﬁcant angular correlations

were expected between ejected nucleons for reactions in which more than one nucleon

were “boiled oﬀ”. However, energetic gamma-ray interactions resulted in comparable

σ(γ,n)and σ(γ,p)cross-section values which were much higher than the single particle

cross sections expected from Courant’s work.

Nucleon-Nucleon correlations inside atomic nuclei 5

Figure 1. Direct demonstration of strongly-correlated 2N clusters (mainly in form of

n-p pairs) by diﬀerent incident particles.

Figure 2. Other direct and indirect manifestations of strongly-correlated 2N systems

inside nuclei.

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Nucleon-nucleoncorrelationsinsideatomicnuclei:synergies,observationsandtheoreticalmodelsRanjeetDalal1,andI.J.DouglasMacGregor21GuruJambheshwarUniversityofScienceandtechnology,Hisar,India2SUPASchoolofPhysicsandAstronomy,UniversityofGlasgow,GlasgowG128QQ,UnitedKingdomE-mail:ranjeet@gjust.orgAugust2022...

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Nucleon-nucleon correlations inside atomic nuclei synergies observations and theoretical models Ranjeet Dalal1 and I.J. Douglas MacGregor2

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