EVALUACIÓN TEÓRICA DE LA DISPERSIÓN INELÁSTICA

DE LEPTONES DE EFECTOS NUCLEARES

Wana, Ngadda, Yakubu.

ISSN 2477-9105

Número 29 Vol.1 (2023)

DOI: https://doi.org/10.47187/perf.v1i29.203

University of Maiduguri, Department of Physics, P.M.B 1069, Maiduguri, Borno State. Nigeria. West Africa.

* emmalikta2014@gmail.com

La dispersión inelásca es un proceso en el que no se conserva la energía cinéca de una parcula

incidente debido a la interacción entre un electrón y un fotón provocando un estado nuclear inestable.

En una interacción del fotón incidente con la materia se produce dispersión Raman donde la frecuencia

del fotón se desplaza hacia al rojo o el azul. La dispersión de electrones de naturaleza profundamente

inelásca que emana de los protones proporciona la evidencia primordial de la presencia de quarks, los

neutrones sufren dispersión inelásca que excita al núcleo y hace que emita parculas corpusculares

y electromagnécas. El objevo de este trabajo fue obtener teóricamente el efecto nuclear sobre la

dispersión de leptones ineláscos y observar la dependencia nuclear. Se ulizaron los métodos, función

de transferencia del momento al cuadrado y el producto escalar de Lorentz. Se obtuvo la correlación

entre los parámetros de baja energía y la valencia de quarks, el valor indicavo en cromodinámica

cuánca es el 5% y el material nuclear innito no conduce a ningún informe de tamaño nito. El origen

de los efectos nucleares aún no se evidencia; sin embargo, las funciones estructurales y los efectos de

tamaño nito fueron probados teóricamente.

Palabras Clave: 



Inelasc scaering is a process in which the kinec energy of an incident parcle is not conserved

due to the interacon between an electron and a photon causing an unstable nuclear state. Upon

the interacon of the incident photon with maer, Raman scaering occurs where the frequency of

the photon shis towards red or blue. Electron scaering of a profoundly inelasc nature emanang

from protons provides the primary evidence for the presence of quarks, neutrons undergo inelasc

scaering that excites the nucleus and causes it to emit corpuscular and electromagnec parcles. The

aim of this work was to theorecally obtain the nuclear eect on the scaering of inelasc leptons and

to observe the nuclear dependence. The methods, cross-secon four-momentum transfer squared

funcon and the Lorentz scalar product, were used. The correlaon between low energy parameters

and quark valence was obtained, the indicave value in quantum chromodynamics is 5% and innite

nuclear material does not lead to any nite size report. The origin of the nuclear eects is not yet

evident; however, the structural funcons and the eects of nite size were theorecally tested.

Keyword: .

EVALUACIÓN TEÓRICA DE LA DISPERSIÓN INELÁSTICA DE

LEPTONES DE EFECTOS NUCLEARES

RESUMEN

ABSTRACT

Theorecal Evaluaon on Inelasc Lepton Scaering

of Nuclear Eects

Fecha de recepción: 10-04-2022 Fecha de aceptación: 18-04-2022 Fecha de publicación: 31-03-2023

Emmanuel Wana Likta *

Y. H. Ngadda

Nura Yakubu

http://ceaa.espoch.edu.ec:8080/revista.perﬁles/

ISSN 2477-9105

Número 29 Vol.1 (2023)

DOI: https://doi.org/10.47187/perf.v1i29.203

EVALUACIÓN TEÓRICA DE LA DISPERSIÓN INELÁSTICA

DE LEPTONES DE EFECTOS NUCLEARES

Wana, Ngadda, Yakubu.

ISSN 2477-9105

Número 29 Vol.1 (2023)

DOI: https://doi.org/10.47187/perf.v1i29.203

I. INTRODUCCIÓN

Inelasc scaering is a fundamental scaering

process in which the kinec energy of an incident

parcle is not conserved. In contrast to elasc

scaering some of the incident parcle energy

is lost or increased (1). The principle of inelasc

collision in dynamics is quite disnct; inelasc

collision in dynamics refers to processes in

which the total macroscopic kinec energy is

not conserved (2). Scaering due to inelasc

collisions will be inelasc but elasc collisions

oen transfer kinec energy between parcles.

As in Compton, scaering due to elasc collisions

can also be inelasc (3).

The inelasc scaering probability that depends

on the incident electron energy is usually smaller

than the elasc scaering one (4). In regard to gas

electron diracon (GED), reecon high-energy

electron diracon (RHEED), and transmission

electron diracon (5). The incident electron

energy is high, and the contribuon of inelasc

electron scaering can be ignored (6). Deep

inelasc scaering of electrons from protons

provided the rst direct evidence of quark

existence (7).

Raman scaering, also known as inelasc

scaering due to a photon being the incident

parcle (8). The incident photon interacts with

maer and the photon frequency is shied

toward red or blue (9). A red shi can be observed

when part of the photon energy is transferred

to the interacng maer, where it adds to its

internal energy through a process (10). The blue

shi can be observed when the internal energy of

the maer is transferred to the photon. The red

and blue shi processes are known as Stokes and

an-stokes Raman Scaering respecvely (11).

Inelasc scaering is the interacon between

an electron and a photon. A high-energy photon

collides with a free electron and transfers energy

(12). An electron with relavisc energy collides

with an infrared or visible photon, the electron

gives energy to the photon (13).

It is known that neutrons undergo many types

of scaering, including both elasc and inelasc

scaering. Whether elasc or inelasc scaer

occurs depends on the neutron speed; fast,

thermal, or somewhere in between (14). It also

depends on the nucleus it strikes and its neutron

cross-secon (15). The neutron interacts with the

nucleus and the system's kinec energy changes

II. MATERIALS AND METHOD

The cross-secon has a four-momentum transfer

squared funcon carried by the virtual photon

and the Lorentz scalar product (19). For a quark

to carry a fracon x of the nucleon momentum

with when probed with resoluon 1

QƐ

This can be jused in quantum chromodynamics

since anything can be jused in a theory that has

not been solved (20). The successful predicon

that the same quark distribuons are given

simply by the square averages of relevant quark

changes (21).

An integral which measures the excess of

fermions over anfermions in the nucleon should

be equal to three (22). Finally, the black box

²)) is the Fourier transform of the light cone

correlaon funcon²)) renormalized at ²

that is calculated in terms of α (²).

Explicitly,

Where

Is dened for a nucleon at rest, with

q(x,Q²)

X = (2)

(1)

in rest frame = 0



X = =(3)

 5

 18





in the inelasc scaering (16). It oen acvates

the nucleus pung it into an excited unstable

short-lived energy state which causes it to quickly

emit some kind of radiaon to bring it back down

to a stable or ground state. Alpha, beta, gamma,

and protons may be emied (17). It is known in

Nuclear Physics that scaered Parcles are a type

of nuclear reacon that can cause the nucleus to

recoil in other direcons (18).

(4)

(5)

(6)

(7)

EVALUACIÓN TEÓRICA DE LA DISPERSIÓN INELÁSTICA

DE LEPTONES DE EFECTOS NUCLEARES

Wana, Ngadda, Yakubu.

ISSN 2477-9105

Número 29 Vol.1 (2023)

DOI: https://doi.org/10.47187/perf.v1i29.203

Where  and are quark eld operaons.

The quark contribuon reduces the equal-me

correlaon funcon of non-relavisc quantum

mechanics (23). A familiar funcon is:

Where │A represents a nucleus at rest and Ψ is

the nucleon eld operator (24).The alternave

representaon as a displaced overlap funcon

Where Ψ is the one nucleon wave funcon,

understanding that the correlaon fracon

measures the system size (25).

(8)

(9)

(11)

(12)

(13)

(14)

(10)

Considering the Rayleigh-Schrödinger

perturbaon theory, the energy dierence is:

Tends to zero as v with  and Q xed. The

only change in the formalism is that with nuclear

target x is usually replaced by

Which can, in principle range from 0 to A. It is

known that for x 0.3 there are no sea quarks

and therefore:

Thus  )must have the form since the quark

per nucleon is xed:

So  ) must be posive in some, if not all the

regions x <0.3.

III. RESULTS AND DISCUSSION

Table 1:

Table 2:

Table 3:

ZQuark Valence

X Y

045

1 2.9 3.9

2 0.4 2.1

3 0.1 2

4-1.9

5 - 1.8

6- 1.7

7 - 1.6

8- 1.5

9-1.4

w Innite Nuclear

g H I J

31 2 1.7 1.3 1.2

40 1.8 1.55 1.35 1.3

50 1.6 1.5 1.36 1.32

60 1.5 1.45 1.37 1.35

70 1.4 1.38 1.38 1.36

80 1.37 1.37 1.37 1.37

90 1.36 1.36 1.39 1.38

100 1.35 1.35 1.4 1.39

Q² Quantum Chromodynamic

A B

58-

6 8 -

711 12.5

8 11 12

11 9 10

13 10 9

14 9.5 8.5

15 9 8

16 5 7.5

20 7 6.5

22 6 6

24 5.7 5.7

26 5 5.7

28 4.95 4.95

29 4.7 4.7

32 3 4.5

34 4.5 4

36 2.5 2.8

38 3 2.5

39 4 2

42 8 -

44 12.5 -

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DE LEPTONES DE EFECTOS NUCLEARES

Wana, Ngadda, Yakubu.

ISSN 2477-9105

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DOI: https://doi.org/10.47187/perf.v1i29.203

Table 4:

Fig. 1:         



Fig. 4:         



Fig. 2:



Fig. 3:



QStructure function

F D

0.5 20 -

0.6 19.9 20

0.75 10 11

158

1.5 37.5

2 3 7.5

2.5 37.5

3 3 7.5

Fig 1 shows that X and Y are parallel lines that

move in opposite lines. Where x represents x >

0.1 and Y represents x 0. Also, gure 4 indicates

a valence correlaon achieved for low energy

parameters for the quark valence correlaon.

Proving that the long-range tail was assumed to

acquit as  that is returned by if this lace is cut

by a quiet calculaon to the rootage which cutsx

 . The    quark valence distribuon

is checked by distances < , the correlaon

funcon spilling for     and necessary

unaltered deportment which obtains the lower

curve. The gure is the product of table 1.

Fig 2 shows that g, H, I and J have a meeng

point which is at 80 on the w axis. It started at

a parallel point that meets the point. Also, the

gure indicates innite nuclear maer so again

it is enrely unreliable for  40. It leads to no

report of nite size eects and an eort was

made to prove the fact that response takes place

theorecally. The gure is ploed from the results

obtained in table 2.

Fig 3 shows that line A forms a zigzag line which

makes it like the leers m and w. While line B

indicates a slight slope also similar to the leer m.

A represents the equaon and B represents

the equaon . This also indicates that there

are errors that quantavely work within. If ² is

chosen to be lile, then that is needed also

becomes lile. The lile value stated in Quantum

Chromodynamics signies that / is nearly

5%. The gure is the product of table 3.

Fig 4 shows F and D lines starng at a point where

a slope from 13 points on the structure-funcon

that are separated from each other. Point 13

EVALUACIÓN TEÓRICA DE LA DISPERSIÓN INELÁSTICA

DE LEPTONES DE EFECTOS NUCLEARES

Wana, Ngadda, Yakubu.

ISSN 2477-9105

Número 29 Vol.1 (2023)

DOI: https://doi.org/10.47187/perf.v1i29.203

indicates that D has a higher structure funcon

than F. D represents Deuterium on the structure

funcon and F represents Fe. Also, the gure

indicates the success of the scaling law that is

in relaon to the deuterium structure-funcon

The heavier can be understood in terms of

qualifying the properes of individual nucleons.

It is coherent to write the X>0.3 region in terms of

individual nucleon donaon since it is restrained

by lesser distances. The gure is ploed from the

results obtained in table 4.

In nuclei, the quarks correlaon funcons have a

large range. Regarding the origin of the nuclear

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IV. CONCLUSIONS

V. REFERENCE

eect, there is no consensus. When the dust

seles, there will be an enhancement at low x,

although it may be closer to the boom than the

top. Pion indicates a natural qualitave view of

this enhancement. Based on pre-exisng nuclear

theory without any addional ingredients.

However, pions are only eecve degrees of

freedom, and an inelasc model will not work

with a high degree of accuracy. This eect is due

to the properes modicaon of nucleons that

are stretched in the nucleus. Structure funcons

have been understood for individual nucleons.

Finite size eects were theorecally proven.

EVALUACIÓN TEÓRICA DE LA DISPERSIÓN INELÁSTICA

DE LEPTONES DE EFECTOS NUCLEARES

Wana, Ngadda, Yakubu.

ISSN 2477-9105

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