Atomic nucleus Coulomb energy and modification of protons
The problem of the experimental determination of the atomic nucleus Coulomb energy is discussed. The expression for the contribution of the proton modification to Coulomb energy is proposed.
Gespeichert in:
| Datum: | 2001 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
|
| Schriftenreihe: | Вопросы атомной науки и техники |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/78447 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Atomic nucleus Coulomb energy and modification of protons / A.Yu. Buki // Вопросы атомной науки и техники. — 2001. — № 1. — С. 59. — Бібліогр.: 7 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-78447 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-784472015-03-18T03:01:55Z Atomic nucleus Coulomb energy and modification of protons Buki, A.Yu. Nuclear reactions The problem of the experimental determination of the atomic nucleus Coulomb energy is discussed. The expression for the contribution of the proton modification to Coulomb energy is proposed. 2001 Article Atomic nucleus Coulomb energy and modification of protons / A.Yu. Buki // Вопросы атомной науки и техники. — 2001. — № 1. — С. 59. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 21.10 Sf. http://dspace.nbuv.gov.ua/handle/123456789/78447 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Nuclear reactions Nuclear reactions |
| spellingShingle |
Nuclear reactions Nuclear reactions Buki, A.Yu. Atomic nucleus Coulomb energy and modification of protons Вопросы атомной науки и техники |
| description |
The problem of the experimental determination of the atomic nucleus Coulomb energy is discussed. The expression for the contribution of the proton modification to Coulomb energy is proposed. |
| format |
Article |
| author |
Buki, A.Yu. |
| author_facet |
Buki, A.Yu. |
| author_sort |
Buki, A.Yu. |
| title |
Atomic nucleus Coulomb energy and modification of protons |
| title_short |
Atomic nucleus Coulomb energy and modification of protons |
| title_full |
Atomic nucleus Coulomb energy and modification of protons |
| title_fullStr |
Atomic nucleus Coulomb energy and modification of protons |
| title_full_unstemmed |
Atomic nucleus Coulomb energy and modification of protons |
| title_sort |
atomic nucleus coulomb energy and modification of protons |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2001 |
| topic_facet |
Nuclear reactions |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/78447 |
| citation_txt |
Atomic nucleus Coulomb energy and modification of protons / A.Yu. Buki // Вопросы атомной науки и техники. — 2001. — № 1. — С. 59. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT bukiayu atomicnucleuscoulombenergyandmodificationofprotons |
| first_indexed |
2025-07-06T02:32:36Z |
| last_indexed |
2025-07-06T02:32:36Z |
| _version_ |
1836863095373299712 |
| fulltext |
ATOMIC NUCLEUS COULOMB ENERGY
AND MODIFICATION OF PROTONS
A.Yu. Buki
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The problem of the experimental determination of the atomic nucleus Coulomb energy is discussed. The expres-
sion for the contribution of the proton modification to Coulomb energy is proposed.
PACS: 21.10 Sf.
Coulomb energy EC of nucleus (the total electro-stat-
ic energy of the interaction of the intranuclear charges)
can be determined from calculation relied on the func-
tion of density charge distribution in the nucleus ρ(r).
Since usually the explicit form of the function ρ(r) fol-
lows from any model of nucleus then the calculation of
the EC is model in character. The single known equation
for Coulomb energy of nucleus expressing this quantity
in terms of the experimental data at once can be taken
from paper [1]. In the representation of paper [2] this
equation has the form
EC = e2 π−1{I1 + I2}, (1)
I1 ≅ Z2 ∫
∞
0
2 d)( qqF , (1a)
I2 ≅ ∫
∞
−
0
22 d)](Z)([ qqGqSin . (1b)
Here e is the elementary electric charge, Z is charge
number of the nucleus, q is the 3-momentum transfer,
F(q) is the longitudinal nuclear form-factor, G(q2) is
proton electric form-factor, Sin(q) is longitudinal re-
sponse function zero moment (The moment Sin(q), as in
[1] and [2], is not normalized on G2(q2)).
The equation (1) was practically used in the experi-
mental papers [2] and [3], where the EC of the 6Li and
12C nuclei were evaluated. The subsequent measure-
ments of the Sin(q) in the region of high momentum
show the necessity of the revision of the Eq.(1) interpre-
tation.
One can see from Eq. (1), the problem of the EC
evaluation is that to calculate I1 and I2 integrals. So, it is
necessary to have the F2(q)- and Sin(q)-data in the wide
momentum region.
The F2(q) quickly decreases with elevation of q, that
permits to bound the range of necessary F2(q)-data and,
consequently, the upper limit of the integral I1 to bound
by q ≈ 1.5 Fm−1. In the case q ≥ 2 Fm−1 the electron scat-
tering on nucleus is quasi-elastic ones scattering on nu-
cleons, and therefore it would be expected that Sin(q) =
ZG2(q2) at these momenta. So, the range of the neces-
sary Sin(q)-data can be bounded by q ≈ 2 Fm−1. In this
approximation the papers [2] and [3] were fulfilled.
However, later experiments (e.g. see [4]) performed
as high as q ≈ 3 Fm−1 show that even thought the ratio
Sin(q)/[ZG2(q2)] = const at q ≥ 2 Fm−1, but it is less than
unity and decreases with elevation of the atomic num-
ber. This phenomenon may be explained by modifica-
tion of all or part nuclear protons, in the result of which
the square on the form-factor of such protons
g2(q2) < G2(q2) (see [5]). In this case the term ZG2(q2) in
Eq.(1b) transforms into some function f(g) to which
tends the Sin(q) with elevation of q. In approach of [6]
f(g) = Z[(1 − D)G2(q2) + Dg2(q2)], (2)
where D is the relative part of modified protons in the
nucleus. The contribution of the protons modification in
the EC according to Eq.(2) has form
∆EC = ∫
∞
−
0
2222
2
d)]()([Z
π
qqgqGDe
. (3)
Using this equation and results of paper [6], we evaluate
that ∆EC > 0 and it equals to 0.04, 0.27, 9.1 MeV for the
nuclei 4He, 12C, 208Pb, correspondingly, that accounts for
∼ 5-50 % of the early e2π−1I2 value of the considerable
nuclei or 2.5-1 % of the total Coulomb energy EC. Other
models of the protons modification (D = 1) show the
same order of value ∆EC.
The principal conclusion following from analysis of
the nucleus Coulomb energy problem is that the accura-
cy of the EC determination immediately depends on the
accuracy of the f(g) function, i.e. on the validity of our
insight about the protons properties in the nucleus.
REFERENCES
1. V.D. Efros. Sum rules in the electron scattering by nuclei
// Yad. Fiz. 1973, v. 18, p. 1184-1202 (in Russian).
2. A.Yu. Buki et al. Experimental determination of 6Li
nucleus coulomb energy. // Yad.Fiz., 1977, v. 25,
p. 457-459 (in Russian).
3. A.Yu. Buki et al. Determination of the coulomb en-
ergy from electron scattering experiment. “Particles
and Nuclei − Tenth International Conference”, Hei-
delberg, July 30 -August 3, 1984, v. I, p. A21.
4. A.Yu. Buki et al. Determination of 12C nucleus
coulomb energy from electron scattering // Ukr. Fiz.
Zhurn, 1985, v. 30. p. 499-501 (in Russian).
5. A. Zghiche et al. Longitudinal and transverse re-
sponses in quasi-elastic electron scattering from
208Pb and 4He // Nucl. Phys., 1994, v. A572, p. 513-
559.
6. G. Orlandini and M. Traini. Sum rules for electron-
nucleus scattering // Rep. Prog. Phys. 1991, v. 54,
p. 257-338.
7. A.Yu. Buki. Coulomb sums and modification of nu-
cleons in the atomic nucleus. “Proc. of the 9th Semi-
nar Electromagnetic Interactions of Nuclei at Low
and Medium Energies”, Moscow (to be published).
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 1.
Series: Nuclear Physics Investigations (37), p. 59.
59
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
REFERENCES
|