Journal of Modern Physics, 2013, 4, 459-462

http://dx.doi.org/10.4236/jmp.2013.44064 Published Online April 2013 (http://www.scirp.org/journal/jmp)

Energy Levels of Helium Nucleus

Cvavb Chandra Raju

Department of Physics, Osmania University, Hyderabad, India

Email: cvavbc@gmail.com

Received January 9, 2013; revised February 10, 2013; accepted February 22, 2013

Copyright © 2013 Cvavb Chandra Raju. This is an open access article distributed under the Creative Commons Attribution License,

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

The Helium-4 nucleus is more similar to the Hydrogen atom of atomic physics. In the case of hydrogen atom, there are

many energy levels which were experimentally seen and theoretically explained using non-relativistic quantum me-

chanics. In this note, we use a central potential to derive the energy levels of Helium-4 nucleus. The ground state and

the first few energy levels agree pretty well with experiment. The same potential can be used with nuclei like Oxy-

gen-17 and many more nuclei.

Keywords: Helium-4; Nuclear Energy Levels; Deuteron; Morphed Gravitational Potential

1. Introduction and Formulation of the

Problem

The Deuteron nucleus has no excited states. The ground

state energy of the Deuteron is experimentally found to

be −2.225 MeV and the measured radius of this nucleus

is 2.1 F. This is the distance between the center of mass

and either of the nucleon in the Deuteron nucleus [1].

There are no known solutions of the Schrödinger equa-

tion of this nucleus with Yukawa potential.

Are there any central potentials with which we can

solve the Schrödinger equation for many nuclei such that

their ground state wave functions and excited states can

be obtained? This question led us to a central potential

which is closely related to the gravitational potential en-

ergy.

There is no reason or experimental support to believe

that the universal constant of gravitation G is same for all

values of interacting masses. For interacting masses of

the order of nucleon masses G may not retain its univer-

sality. This led us to the following expression for the

gravitational potential energy of two particles whose

masses are and ,

1

m2

m

2

2

012

gc

GM mm

r

0

1eVr G , (1.1)

where in place of the usual constant of universal constant

G we have a modulating factor.

The constant g2 is a dimensionless real number whereas

has dimensions of mass. We believe that the expo-

nential goes to zero when the interacting masses are large

and the Universal law of Gravitation is restored. It is the

parameter M0 that causes the Universal Law of Gravita-

tion restored. An approximation to Equation (1.1) is giv-

en by,

2

12

2

0

11 mm

gc

Vr Gr

GM

,

(1.2)

where “r” is the distance between the interacting parti-

cles. Simplifying Equation (1.2), we have,

2

12

2

0

mm

gc

Vr r

M

2

0

. (1.3)

The above potential energy is obtained from the gravi-

tational potential energy. It may be called “the morphed

gravitational potential energy”. There are two constants

g2 and

which we will obtain below.

2. Deuteron

The Deuteron is a bound system of a neutron and a pro-

ton with an orbital angular momentum of zero. The total

spin of the two nucleons is one. The deuteron nucleus has

no excited states. The experimentally measured ground

state energy of the Deuteron nucleus is −2.225 MeV and

its orbital angular quantum number . There is no

stable diproton. It is also known that the nuclear potential

depends on the spin orientation [2] of the nucleons inside

a nucleus. If the nuclear force is independent of their spin

orientation then the singlet (total spin = 0) state and the

triplet state (total spin = 1) will have the same energy.

0

C

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