8 Nuclear Force and its Proparties – 6

Sanjay Kumar Chamoli

Learning Outcomes

From this module students may get to know about the following:

The knowledge of basic nuclear properties.
The importance of nuclear properties.
The experimental ways of determining nuclear properties.

1.3 Properties of nuclear interaction

Based on the low-energy properties described in the previous module, we can discuss about many properties of nuclear interaction. Here we can summarize the main features of internucleon force.

Nuclear interaction has the following properties:

Finite range
Intermediate-range attraction
Short-range repulsion (“hard core”)
Spin-dependent non-central forces Tensor force – Spin-orbit force
Charge independence

Finite Range :

Intermediate range attaraction:

Nuclei are bound and the average distance between nucleons in nuclei is ~ 2 fm which roughly corresponds to the range of the attractive force.

Short range repulsion (Hard core) :

Fig. 1: A graph between phase shift and lab. Energy showing the comparison of 1S0 phase shifts to 1D2 phase shifts.

Spin dependent non-central forces:

Tensor force:

The first evidence of tensor component in the nuclear force came from the study of deuteron.

Fig. 2: Oblate and prolate nuclei with spin pointing in the z-direction. Here the nuclei are symmetric along z-direction.

Spin-orbit force:

Fig. 3: Scattering of spin-polarized nucleons indicates that nuclear force has a component which depends on the spin and angular momentum of the interacting nucleon.

Fig. 4: The tensor force in the deuteron is attractive in the cigar-shaped configuration and repulsive in the disk shaped configuration. Two bar magnets provide a classical example of a tensor force.

Symmetry properties of nuclear force

Nuclear interaction must be invariant under translation, called translational invariance.
Interaction may depend on momenta P1 & P2 of two particles, but the only possible term showing this dependence is P = ½ (P1 – P2), called Galilean invariance.
The interaction must remain unchanged under rotation of coordinate system, called rotational invariance.
Also it must assume time-reversal, space reflection (parity) and isospin invariances.

Most general two-body nuclear potential under the symmetry conditions is given by

Fig. 5: Nuclear potential curve showing the nature of potential in different ranges. Nuclear force is repulsive at very short range.

Summary

The nuclear interaction unlike other interactions is a complicated function of various terms.
At short range within the nuclear volume, the force becomes repulsive also.
The nuclear interaction satisfies various symmetry properties, like translational, Galilean and rotational invariance.
The parameters of the nuclear interaction are obtained semi-empirically by fitting the experimental data with some assumed forms.

you can view video on Nuclear Force and its Proparties – 6

References:

Introduction to Nuclear Physics – by Keneth S Krane.
Introductory Nuclear Physics – by Samuel S M Wong.
Nuclear Physics – by R R Roy & B P Nigam.
Elementary Nuclear Theory by Hans A. Bethe and Phillip Morrison.
Introduction to Nuclear Physics, 2nd Edition, W.N.Cottingham & D.A. Greenwood.
Concept of Nuclear Physics by B L Cohen, McGraw Hill.
Nuclear Physics ; an Introduction by S.B. Patel.
The Origin of the Concept of Nuclear Force by L.M. Brown and Rechenberg.
Theoretical Nuclear Physics by John M. Blatt and Victor F. Weisskopf.
Experimental techniques in Nuclear Physics by Dorin N. Poenaru & Walter Greiner
Exotic Nuclear Excitation by S.C. Pancholi
Nuclear spectroscopy Part B, by Fay Ajzenberg- Selove
Theory and Problems of modern Physics (Schaum’s outline Series)
Basic Ideas & Concepts in Nuclear Physics – by K Heyde
The “Particles of Modern Physics” by J. D. Stranathan, Philadephia: Blakiston.
5. Nuclear Physics by Irving Kaplan, Narosa Publishing House.

Web Links

Did you know ?

The nuclear force only acts within the nucleus and within that domain, at long distances, it is attractive while at very short distances it becomes repulsive too.
According to standard model the nuclear force is mediated by massive particles and therefore has finite range.
According to Yukawa theory, the strong interaction between nucleons is mediated by massive particles called mesons (mm ~ 200 me).
In the standard model the nuclear force is not same as the strong force which acts on hadrons. More correctly the nuclear force is the residual strong force.
As per the Standard Model pions and nucleons are made of quarks held together by nuclear (colour) force mediated by gluons.
The residual of nuclear force outside of quark triplets (neutron and proton) holds neutrons and protons together in nuclei.
The Mesons predicted in the Yukawa theory were originally believed to be muons (which have mass ~100 MeV).
Pions (π+, π-, π0) discovered in 1947 interact strongly with nucleons and have masses, (mπ c2 ≈ 140MeV).In the context of the “Standard Model” pions and nucleons are made of quarks held together by nuclear “colour” force mediated by gluons.
The theory of strong interaction is quantum chromo dynamics (QCD).

Biography: