# Hydrogen-like Plasmas under Endohedral Cavity

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Formalism

#### 2.1. Oscillator Strength and Polarizability

#### 2.2. Shannon Entropy

## 3. Result and Discussion

#### 3.1. Critical Screening Constant in DHPWS and ECSCPWS

- At the onset, it should be mentioned that the qualitative behaviour of ${S}_{r}$ with $\lambda $ in DHPWS and ECSCPWS are quite similar.
- Panels (I), (II) in Figure 1 show that there exists at least three bound states in either of the fullerene trapped plasmas. Because, in both cases, circular or node-less states with $\ell \phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}$0–2 are never going to be deleted. As a consequence, no abrupt jump in ${S}_{r}$ is observed. In these states ${S}_{r}$ increases with $\lambda $ and finally converges to the respective limiting values.
- Panels (I), (II) of Figure 2 suggest that, for a given state, there exists a characteristic $\lambda $ at which the ${S}_{r}$ value jumps suddenly, signifying the phase transition. The position of these ${\lambda}^{\left(c\right)}$ gets right shifted with a rise in Z. Here, a first order phase transition happens in both the plasmas involving $2s,3s,3p,4d,4f,5f,5g,6g$ states.
- These observations lead us to the conjecture that, in these two fullerene trapped plasmas, phase transition occurs for all $\ell \ge 3$ states. However, for $\ell \phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}$0–2 states, a similar phenomenon occurs only when $(n-\ell -1)\ge 1$.

#### 3.2. Dipole Oscillator Strength

#### 3.3. Polarizability

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Plot of ${S}_{r}$ as function of $\lambda $ for $1s,2p,3d$ states; bottom (I) and top (II) panels refer to DHPWS and ECSCPWS, having $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$. See text for details.

**Figure 2.**Plot of ${S}_{r}$ as function of $\lambda $ for $2s,3s,3p,4d,4f,5f,5g,6g$; bottom (I) and top (II) panels refer to DHPWS and ECSCPWS, having $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$. See text for details.

**Figure 3.**Plot of ${f}^{\left(1\right)}$ as function of $\lambda $ in DHPWS potential for selected transitions mentioned in the panels (

**a**–

**h**), for $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$. See text for details.

**Figure 4.**Plot of ${f}^{\left(1\right)}$ as function of $\lambda $ in ECSCPWS potential for selected transitions mentioned in the panels, for $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$. See text for details.

**Figure 5.**Plot of ${\alpha}^{\left(1\right)}$ as function of $\lambda $ in DHPWS potential, for $1s,2s,2p$ states as mentioned in the panels, for $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$. See text for details.

**Figure 6.**Plot of ${\alpha}^{\left(1\right)}$ as function of $\lambda $ in ECSCPWS potential, for $1s,2s,2p$ states as mentioned in the panels, for $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$. See text for details.

**Table 1.**Calculated ${\lambda}_{n,\ell}^{\left(c\right)}$ for H-like ions for $1s,2s,3s,2p,3p,3d,4d,4f,5f,5g,6g$ states in DHPWS and ECSCPWS ($L\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,N\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}300$). See text for details.

DHPWS | ECSCPWS | ||||||
---|---|---|---|---|---|---|---|

$\mathit{Z}$ | State | ${\mathit{\lambda}}_{\mathit{n},\ell}^{\left(\mathit{c}\right)}$ | ${\mathcal{E}}_{\mathit{n},\ell}$ | $\mathit{Z}$ | State | ${\mathit{\lambda}}_{\mathit{n},\ell}^{\left(\mathit{c}\right)}$ | ${\mathcal{E}}_{\mathit{n},\ell}$ |

1 | $1s$ | − | − | 1 | $1s$ | − | − |

2 | − | − | 2 | − | − | ||

1 | $2s$ | $0.9111{\phantom{\rule{3.33333pt}{0ex}}}^{a}$ | −0.000000254 | 1 | $2s$ | 0.6287 | −0.000000038 |

2 | 2.1247 | −0.000000197 | 2 | 1.3618 | −0.000000165 | ||

1 | $3s$ | $0.1565{\phantom{\rule{3.33333pt}{0ex}}}^{a}$ | −0.000000439 | 1 | $3s$ | 0.0762 | −0.000000130 |

2 | 0.3900 | −0.000000055 | 2 | 0.2688 | −0.000000238 | ||

1 | $2p$ | − | − | 1 | $2p$ | − | − |

2 | − | − | 2 | − | − | ||

1 | $3p$ | $0.1160{\phantom{\rule{3.33333pt}{0ex}}}^{a}$ | −0.000000096 | 1 | $3p$ | 0.0730 | −0.000001331 |

2 | 0.3575 | −0.000011586 | 2 | 0.2633 | −0.000053585 | ||

1 | $3d$ | − | − | 1 | $3d$ | − | − |

2 | − | − | 2 | − | − | ||

1 | $4d$ | 0.0732 | −0.000000291 | 1 | $4d$ | 0.0466 | −0.000003059 |

2 | 0.1197 | −0.000005269 | 2 | 0.0782 | −0.000064445 | ||

1 | $4f$ | 0.1947 | −0.000000856 | 1 | $4f$ | 0.1267 | −0.000007139 |

2 | 0.2994 | −0.000023163 | 2 | 0.1681 | −0.000018290 | ||

1 | $5f$ | 0.0472 | −0.000016099 | 1 | $5f$ | 0.0323 | −0.000001631 |

2 | 0.0831 | −0.000007057 | 2 | 0.0540 | −0.000038551 | ||

1 | $5g$ | 0.0333 | −0.000000778 | 1 | $5g$ | 0.0278 | −0.000006697 |

2 | 0.1231 | −0.000005413 | 2 | 0.0903 | −0.000078050 | ||

1 | $6g$ | 0.0288 | −0.000005039 | 1 | $6g$ | 0.0210 | −0.000001928 |

2 | 0.0588 | −0.000040341 | 2 | 0.0403 | −0.000068680 |

**Table 2.**${f}^{\left(1\right)}$ values for DHPWS and ECSCPWS for fixed ${r}_{c}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}7.7,8$ and $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$, using $L=1$ and $N=300$.

Transition | $\mathit{\lambda}$ | DHPWS | ECSCPWS | ||||||
---|---|---|---|---|---|---|---|---|---|

${\mathit{r}}_{\mathit{c}}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{7.7}$ | ${\mathit{r}}_{\mathit{c}}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{8}$ | ${\mathit{r}}_{\mathit{c}}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{7.7}$ | ${\mathit{r}}_{\mathit{c}}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{8}$ | ||||||

$\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{1}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{2}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{1}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{2}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{1}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{2}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{1}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{2}$ | ||

1s→2p | 0.01 | 0.472909 | 0.405489 | 0.393008 | 0.399455 | 0.473031 | 0.405670 | 0.393153 | 0.399658 |

0.1 | 0.463893 | 0.389264 | 0.382538 | 0.380980 | 0.466412 | 0.399214 | 0.385322 | 0.392167 | |

0.5 | 0.506522 | 0.146559 | 0.445168 | 0.104184 | 0.506896 | 0.062774 | 0.475507 | 0.036498 | |

1.0 | 0.859970 | 0.072607 | 0.881023 | 0.047763 | 0.941505 | 0.069773 | 0.911234 | 0.051167 | |

2.5 | 0.937700 | 0.910538 | 0.902761 | 0.915478 | 0.918853 | 0.924631 | 0.884901 | 0.889980 | |

2p→1s | 0.01 | −0.157636 | −0.135163 | −0.131002 | −0.133151 | −0.157677 | −0.135223 | −0.131051 | −0.133219 |

0.1 | −0.154631 | −0.129754 | −0.127512 | −0.126993 | −0.155470 | −0.133071 | −0.128440 | −0.130722 | |

0.5 | −0.168840 | −0.048853 | −0.148389 | −0.034728 | −0.168965 | −0.020924 | −0.158502 | −0.012166 | |

1.0 | −0.286656 | −0.024202 | −0.293674 | −0.015921 | −0.313835 | −0.023257 | −0.303744 | −0.017055 | |

2.5 | −0.312566 | −0.303512 | −0.300920 | −0.305159 | −0.306284 | −0.308210 | −0.294967 | −0.296660 | |

2p→3d | 0.01 | 1.088693 | 0.800227 | 1.082666 | 0.732754 | 1.088689 | 0.800197 | 1.082677 | 0.732695 |

0.1 | 1.088778 | 0.806429 | 1.081425 | 0.743057 | 1.088627 | 0.798441 | 1.081926 | 0.731705 | |

0.5 | 1.071869 | 1.055338 | 1.054450 | 1.060247 | 1.055825 | 1.067797 | 1.036342 | 1.050053 | |

1.0 | 1.052710 | 1.063993 | 1.034850 | 1.045177 | 1.039857 | 1.036862 | 1.023702 | 1.020954 | |

2.5 | 1.043849 | 1.044600 | 1.027258 | 1.027832 | 1.042933 | 1.042720 | 1.026567 | 1.026410 | |

3d→2p | 0.01 | −0.653216 | −0.480136 | −0.649599 | −0.439652 | −0.653213 | −0.480118 | −0.649606 | −0.439617 |

0.1 | −0.653267 | −0.483857 | −0.648855 | −0.445834 | −0.653176 | −0.479064 | −0.649156 | −0.439023 | |

0.5 | −0.643121 | −0.633202 | −0.632670 | −0.636148 | −0.633495 | −0.640678 | −0.621805 | −0.630032 | |

1.0 | −0.631626 | −0.638396 | −0.620910 | −0.627106 | −0.623914 | −0.622117 | −0.614221 | −0.612572 | |

2.5 | −0.626309 | −0.626760 | −0.616355 | −0.616699 | −0.625760 | −0.625632 | −0.615940 | −0.615846 | |

3d→4f | 0.01 | 1.361677 | 1.378364 | 1.350361 | 1.374690 | 1.361703 | 1.378352 | 1.350391 | 1.374693 |

0.1 | 1.359552 | 1.378857 | 1.347923 | 1.373824 | 1.360468 | 1.378527 | 1.348914 | 1.374145 | |

0.5 | 1.342821 | 1.355667 | 1.330534 | 1.342513 | 1.333760 | 1.336163 | 1.321648 | 1.322866 | |

1.0 | 1.334518 | 1.337464 | 1.322958 | 1.325371 | 1.329986 | 1.328230 | 1.319261 | 1.317836 | |

2.5 | 1.331894 | 1.331979 | 1.320806 | 1.320868 | 1.331802 | 1.331794 | 1.320741 | 1.320736 |

**Table 3.**${f}^{\left(1\right)}$ values for DHPWS and ECSCPWS for ${r}_{c}\to \infty $ and $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$, using $L=1$ and $N=300$.

Transition | DHPWS | ECSCPWS | ||||||
---|---|---|---|---|---|---|---|---|

$\mathit{\lambda}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{1}$ | $\mathit{\lambda}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{2}$ | $\mathit{\lambda}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{1}$ | $\mathit{\lambda}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{2}$ | |

1s→2p | 0.01 | 0.149983 | 0.01 | 0.377669 | 0.01 | 0.150086 | 0.01 | 0.378002 |

0.1 | 0.143844 | 0.1 | 0.345192 | 0.1 | 0.143408 | 0.1 | 0.363852 | |

0.5 | 0.405345 | 0.5 | 0.014097 | 0.5 | 0.795304 | 0.5 | 0.003368 | |

1.0 | 0.853185 | 1.0 | 0.008094 | 1.0 | 0.815081 | 1.0 | 0.015977 | |

2.5 | 0.813876 | 2.5 | 0.829531 | 2.5 | 0.809188 | 2.5 | 0.810333 | |

2p→1s | 0.01 | −0.049994 | 0.01 | −0.125889 | 0.01 | −0.050028 | 0.01 | −0.126000 |

0.1 | −0.047948 | 0.1 | −0.115064 | 0.1 | −0.047802 | 0.1 | −0.121284 | |

0.5 | −0.135115 | 0.5 | −0.004699 | 0.5 | −0.265101 | 0.5 | −0.001122 | |

1.0 | −0.284395 | 1.0 | −0.002698 | 1.0 | −0.271693 | 1.0 | −0.005325 | |

2.5 | −0.271292 | 2.5 | −0.276510 | 2.5 | −0.269729 | 2.5 | −0.270111 | |

2p→3d | 0.01 | 1.062893 | 0.01 | 0.511654 | 0.01 | 1.062940 | 0.01 | 0.511243 |

0.1 | 1.059233 | 0.1 | 0.563033 | 0.1 | 1.061126 | 0.1 | 0.525528 | |

0.5 | 1.039334 | 0.5 | 1.058267 | 0.5 | 1.033436 | 0.5 | 1.037782 | |

1.0 | 1.032612 | 1.0 | 1.035607 | 1.0 | 1.029282 | 1.0 | 1.028293 | |

2.5 | 1.030470 | 2.5 | 1.030594 | 2.5 | 1.030324 | 2.5 | 1.030294 | |

3d→2p | 0.01 | −0.637736 | 0.01 | −0.306992 | 0.01 | −0.637764 | 0.01 | −0.306745 |

0.1 | −0.635539 | 0.1 | −0.337820 | 0.1 | −0.636675 | 0.1 | −0.315316 | |

0.5 | −0.623600 | 0.5 | −0.634960 | 0.5 | −0.620061 | 0.5 | −0.622669 | |

1.0 | −0.619567 | 1.0 | −0.621364 | 1.0 | −0.617569 | 1.0 | −0.616975 | |

2.5 | −0.618282 | 2.5 | −0.618356 | 2.5 | −0.618194 | 2.5 | −0.618176 | |

3d→4f | 0.01 | 1.358996 | 0.01 | 1.377113 | 0.01 | 1.358989 | 0.01 | 1.377140 |

0.1 | 1.358827 | 0.1 | 1.374730 | 0.1 | 1.358891 | 0.1 | 1.376182 | |

0.176 | 1.352618 | 0.15 | 1.372349 | 0.12602 | 1.354588 | 0.157 | 1.372370 | |

0.1931 | 1.347244 | 0.255 | 1.364948 | 0.12638 | 1.354413 | 0.16724 | 1.369061 | |

0.19462 | 1.346487 | 0.29949 | 1.354689 | 0.12671 | 1.354225 | 0.16812 | 1.368517 |

**Table 4.**${\alpha}^{\left(1\right)}$ values for DHPWS and ECSCPWS for ${r}_{c}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{4pt}{0ex}}7.7\phantom{\rule{4pt}{0ex}}\&\phantom{\rule{4pt}{0ex}}8$ and $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$, using $L=1$ and $N=300$.

State | $\mathit{\lambda}$ | DHPWS | ECSCPWS | ||||||
---|---|---|---|---|---|---|---|---|---|

${\mathit{r}}_{\mathit{c}}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{7.7}$ | ${\mathit{r}}_{\mathit{c}}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{8}$ | ||||||||

Z = 1 | Z = 2 | Z = 1 | Z = 2 | Z = 1 | Z = 2 | Z = 1 | Z = 2 | ||

1s | 0.01 | 4.657831 | 0.28128622 | 4.746857 | 0.2812862 | 4.6554220 | 0.2812521 | 4.7442022 | 0.2812521 |

0.1 | 4.881931 | 0.28451405 | 4.994924 | 0.2845141 | 4.7251882 | 0.2817758 | 4.8232375 | 0.2817759 | |

0.5 | 12.2287 | 0.35794112 | 14.6516 | 0.3579433 | 17.04331 | 0.3321934 | 24.00875 | 0.3321963 | |

1.0 | 78.7749 | 0.69849914 | 140.048 | 0.6990358 | 202.0018 | 1.1380112 | 320.2554 | 1.1591198 | |

2.5 | 230.696 | 128.19895 | 345.626 | 226.2246 | 259.3304 | 251.0688 | 375.0790 | 367.0643 | |

3.0 | 240.868 | 187.73712 | 356.253 | 299.8536 | 260.2497 | 256.3160 | 375.9265 | 372.1057 | |

2s | 0.01 | −6323.6041 | 1974.66567 | 2449.20791 | 1407.62883 | −6259.74897 | 2014.6251 | 2455.03251 | 1427.48523 |

0.1 | −25,299.096 | 762.542243 | 2096.11187 | 671.915445 | −12,087.9810 | 1214.6507 | 2197.55093 | 975.180845 | |

0.5 | 18,546.933 | 297.184946 | 2569.87340 | 369.786944 | 4830.94856 | 368.81438 | 2570.99350 | 481.397967 | |

1.0 | −252.97113 | 421.447127 | −232.042760 | 527.012512 | −26.4762447 | 481.38339 | −9.29681306 | 592.581494 | |

2.5 | 9.5211800 | −128.377389 | 18.4890829 | −86.8752095 | 29.6816393 | 21.677927 | 36.7365367 | 29.6077279 | |

3.0 | 16.629850 | −29.6973425 | 24.7934626 | −13.1804006 | 30.8831256 | 27.068895 | 37.7878081 | 34.3689306 | |

2p | 0.01 | 2191.410 | −643.03504 | −702.8776 | −452.1602 | 2170.076 | −656.3755 | −704.8910 | −458.8075 |

0.1 | 8520.618 | −237.05905 | −579.3616 | −204.1988 | 4114.992 | −388.9010 | −615.7853 | −306.8603 | |

0.5 | −6061.053 | −24.508518 | −694.8934 | −13.59247 | −1473.332 | −1.579597 | −678.1659 | 9.116706 | |

1.0 | 204.2574 | −8.8332529 | 219.5863 | −0.670906 | 100.0618 | −6.121894 | 97.77017 | −1.240847 | |

2.5 | 79.78501 | 152.51948 | 81.67296 | 148.6793 | 67.74707 | 71.51052 | 70.12450 | 73.50398 | |

3.0 | 75.37053 | 102.96430 | 77.42353 | 103.0182 | 67.26899 | 69.03491 | 69.71802 | 71.31396 |

**Table 5.**${\alpha}^{\left(1\right)}$ values for DHPWS and ECSCPWS for ${r}_{c}$→∞ and $Z\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1,\phantom{\rule{0.166667em}{0ex}}2$, using $L=1$ and $N=300$.

State | DHPWS | ECSCPWS | ||||||
---|---|---|---|---|---|---|---|---|

$\mathit{\lambda}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{1}$ | $\mathit{\lambda}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{2}$ | $\mathit{\lambda}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{1}$ | $\mathit{\lambda}$ | $\mathit{Z}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}\mathbf{2}$ | |

1s | 0.01 | 5.041120 | 0.01 | 0.2812863 | 0.01 | 5.0373245 | 0.01 | 0.2812522 |

0.1 | 5.405572 | 0.1 | 0.2845141 | 0.1 | 5.1638458 | 0.1 | 0.2817760 | |

0.5 | 71.4353 | 0.5 | 0.3579454 | 0.5 | 553.3792 | 0.5 | 0.3321994 | |

1.0 | 1076.49 | 1.0 | 0.7000504 | 1.0 | 1241.072 | 1.0 | 1.2523499 | |

2.5 | 1242.28 | 2.5 | 1183.049 | 2.5 | 1257.825 | 2.5 | 1254.207 | |

3.0 | 1247.93 | 3.0 | 1220.684 | 3.0 | 1258.140 | 3.0 | 1256.377 | |

2s | 0.01 | 1480.865 | 0.01 | 871.382822 | 0.01 | 1480.571 | 0.01 | 877.9676 |

0.1 | 1507.894 | 0.1 | 578.058339 | 0.1 | 1497.317 | 0.05 | 845.6145 | |

0.3 | 1720.036 | 0.5 | 1060.98797 | 0.2 | 1587.219 | 0.09 | 738.4854 | |

0.5 | 2721.953 | 1.0 | 1338.07651 | 0.3 | 1771.873 | 0.3 | 940.9011 | |

0.7 | −326.1830 | 1.5 | 1503.41076 | 0.5 | −1276.650 | 0.7 | 1404.159 | |

0.9 | 23008.31 | 2.0 | −23.222516 | 0.6 | 259.9035 | 1.3 | −65.30549 | |

2p | 0.01 | −150.7481 | 0.01 | −262.0658419 | 0.01 | −150.9188 | 0.01 | −264.3678 |

0.1 | −139.2984 | 0.1 | −152.6892619 | 0.1 | −140.9449 | 0.1 | −201.3010 | |

0.5 | −443.5363 | 0.5 | 69.93496507 | 0.5 | 786.5248 | 0.5 | 87.43362 | |

1.0 | 168.1365 | 1.0 | 64.90555224 | 1.0 | 114.3632 | 1.0 | 55.87104 | |

2.5 | 111.5520 | 2.5 | 133.2633406 | 2.5 | 106.2537 | 2.5 | 107.5945 | |

3.0 | 109.6328 | 3.0 | 119.4094711 | 3.0 | 106.1153 | 3.0 | 106.7672 |

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## Share and Cite

**MDPI and ACS Style**

Chowdhury, S.; Mukherjee, N.; Roy, A.K.
Hydrogen-like Plasmas under Endohedral Cavity. *Quantum Rep.* **2023**, *5*, 459-474.
https://doi.org/10.3390/quantum5020030

**AMA Style**

Chowdhury S, Mukherjee N, Roy AK.
Hydrogen-like Plasmas under Endohedral Cavity. *Quantum Reports*. 2023; 5(2):459-474.
https://doi.org/10.3390/quantum5020030

**Chicago/Turabian Style**

Chowdhury, Saptarshi, Neetik Mukherjee, and Amlan K. Roy.
2023. "Hydrogen-like Plasmas under Endohedral Cavity" *Quantum Reports* 5, no. 2: 459-474.
https://doi.org/10.3390/quantum5020030