Vol.07 No.02(2018), Article ID:24986,8 pages
10.12677/CMP.2018.72010

Prediction Estimation on the Results of Totally Polarized Proton Collisions Based on Magnetic Charge Model

Jun Yuan, Ping’an Liu, Xiaolei Li, Li Wang, Ying Liu

Xi’an Institute of Modern Control Technology, Xi’an Shaanxi

Received: Apr. 25th, 2018; accepted: May 15th, 2018; published: May 22nd, 2018

ABSTRACT

The magnetic charge model of totally polarized proton is derived through the correlative quantum theory and magnetics theory. We suppose that under the totally polarized condition the nuclear event and cross section of proton-proton collision relative to normal circumstance will increase evidently so the dynamics in the totally polarized proton-proton collision process is discussed and the concise expression of the ratio of spin magnetic force to Coulomb force, the ratio of nuclear event and the increment of cross section were derived successively. The magnetic charge model of spinning proton and the concise expressions presented can be used in the quantitative analysis of the influence on the nuclear reaction probability which induced by spin magnetic force.

Keywords:Magnetic Charge, Polarized Proton, Nuclear Events, Cross Section

1. 引言

2. 理论模型

${W}_{M}={\mu }_{I}\cdot B$ (1)

WM可取值为所有氢原子能级精细结构 $\Delta E$ 中值最小的 [4] 。因此，核外电子自旋与轨道运动在质子处产生的磁场为

$B=\frac{\Delta E}{{\mu }_{I}}$ (2)

Figure 1. Hydrogen atom model

$H=\frac{{q}_{m}}{4\text{π}{\mu }_{0}{r}^{2}}$ (3)

r可取为波尔半径，即 $r=0.529×{10}^{-10}\text{m}$ ，该场可视为核外电子磁场在质子上的感应场，即

$H=\frac{B}{{\mu }_{0}}$ (4)

$\frac{\Delta E}{{\mu }_{I}{\mu }_{0}}=\frac{{q}_{m}}{4\text{π}{r}^{2}{\mu }_{0}}$ (5)

${q}_{m}=\frac{4\text{π}{r}^{2}\Delta E}{{\mu }_{I}}$ (6)

${F}_{M}=\frac{{q}_{m}^{2}}{4\text{π}{\mu }_{0}{r}^{2}}$ (7)

${F}_{E}=\frac{{q}^{2}}{4\text{π}{\epsilon }_{0}{r}^{2}}$ (8)

${\mu }_{0},{\epsilon }_{0}$ 为真空磁导率和介电常数。因此可导出自旋磁力与库仑力之比为

$\frac{|{F}_{M}|}{|{F}_{E}|}=\frac{{\epsilon }_{0}}{{\mu }_{0}}\cdot \frac{{q}_{m}^{2}}{{q}^{2}}$ (9)

Figure 2. Sketch of particle motion under self-spinning magnetic gravity

S运动后也击中d点质子，即在磁引力作用下反应概率会有所提高，Ra可定义为全极化条件下自旋引力的作用半径。令 $\delta =\frac{|{F}_{M}|}{|{F}_{E}|}-1$ ，δ为磁作用力超出电作用力的比例系数。当圆环上入射的质子能量为E0时，其x向位移与y向位移大致有如下关系

$x={V}_{0}\sqrt{\frac{2y{m}_{p}}{{F}_{\delta }}}$ (10)

${F}_{\delta }=\delta {F}_{M}=\frac{\delta {q}_{m}^{2}}{4\text{π}{\mu }_{0}\left[{\left(L-x\right)}^{2}+{y}^{2}\right]}$ (11)

${L}^{2}={R}_{a}^{3}\frac{8\text{π}{\mu }_{0}{m}_{p}{V}_{0}^{2}}{\delta {q}_{m}^{2}}$ (12)

${R}_{a}=\sqrt[3]{\frac{\delta {L}^{2}{q}_{m}^{2}}{8\text{π}{\mu }_{0}{m}_{p}{v}_{0}^{2}}}=\sqrt[3]{\frac{\delta {L}^{2}{q}_{m}^{2}}{8\text{π}{\mu }_{0}{E}_{0}}}$ (13)

$\zeta =\frac{\text{π}{R}_{a}}{r}$ (14)

$P=1-\frac{1}{{\text{e}}^{\sigma Nx}}$ (15)

$\zeta ={P}_{2}/{P}_{1}=\frac{{\text{e}}^{{\sigma }_{1}Nx}\left({\text{e}}^{{\sigma }_{2}Nx}-1\right)}{{\text{e}}^{{\sigma }_{2}Nx}\left({\text{e}}^{{\sigma }_{1}Nx}-1\right)}$ (16)

$\Delta \sigma ={\sigma }_{2}-{\sigma }_{1}=-\frac{\mathrm{ln}\left[{\text{e}}^{{\sigma }_{1}Nx}-\left({\text{e}}^{{\sigma }_{1}Nx}-1\right)\zeta \right]}{Nx}$ (17)

3. 算例

3.1. 模型校验

Figure 3. Comparison between the calculated results and RHIC experimental data

3.2. 自旋引起的反应截面增量分析

Figure 4. The error curve of experimental data

Figure 5. p-p scattering cross section in unpolarized state

Figure 6. p-p scattering cross section in polarized state

Figure 7. p-p nuclear reaction event in polarized state

3.3. 自旋对低能区反应概率的影响

4. 结束语

Figure 8. The relationship between the incident nuclear events and the incident proton energy in the low energy region

Prediction Estimation on the Results of Totally Polarized Proton Collisions Based on Magnetic Charge Model[J]. 凝聚态物理学进展, 2018, 07(02): 76-83. https://doi.org/10.12677/CMP.2018.72010

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