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PROPN iajs-3455 3 39 mohammed1 mohammed1 PROPN iajs-3455 3 40 , , PUNCT iajs-3455 3 41 * * PUNCT iajs-3455 3 42 and and CCONJ iajs-3455 3 43 ali ali PROPN iajs-3455 3 44 d. d. PROPN iajs-3455 3 45 salloum2 salloum2 PROPN iajs-3455 4 1 1,2department 1,2department NUM iajs-3455 4 2 of of ADP iajs-3455 4 3 physics physics PROPN iajs-3455 4 4 , , PUNCT iajs-3455 4 5 college college NOUN iajs-3455 4 6 of of ADP iajs-3455 4 7 sciences science NOUN iajs-3455 4 8 for for ADP iajs-3455 4 9 women woman NOUN iajs-3455 4 10 , , PUNCT iajs-3455 4 11 university university NOUN iajs-3455 4 12 of of ADP iajs-3455 4 13 baghdad baghdad PROPN iajs-3455 4 14 , , PUNCT iajs-3455 4 15 baghdad baghdad PROPN iajs-3455 4 16 , , PUNCT iajs-3455 4 17 iraq iraq PROPN iajs-3455 4 18 . . PUNCT iajs-3455 5 1 * * PUNCT iajs-3455 5 2 corresponding correspond VERB iajs-3455 5 3 author author NOUN iajs-3455 5 4 received receive VERB iajs-3455 5 5 : : PUNCT iajs-3455 5 6 2 2 NUM iajs-3455 5 7 may may PROPN iajs-3455 5 8 2023 2023 NUM iajs-3455 5 9 accepted accept VERB iajs-3455 5 10 : : PUNCT iajs-3455 5 11 7 7 NUM iajs-3455 5 12 june june PROPN iajs-3455 5 13 2023 2023 NUM iajs-3455 5 14 published publish VERB iajs-3455 5 15 : : PUNCT iajs-3455 5 16 20 20 NUM iajs-3455 5 17 october october NOUN iajs-3455 5 18 2024 2024 NUM iajs-3455 5 19 345510.30526/37.4.doi.org/ 345510.30526/37.4.doi.org/ NUM iajs-3455 5 20 abstract abstract ADJ iajs-3455 5 21 the the DET iajs-3455 5 22 level level NOUN iajs-3455 5 23 density density NOUN iajs-3455 5 24 is be AUX iajs-3455 5 25 a a DET iajs-3455 5 26 parameter parameter NOUN iajs-3455 5 27 that that PRON iajs-3455 5 28 has have VERB iajs-3455 5 29 great great ADJ iajs-3455 5 30 importance importance NOUN iajs-3455 5 31 in in ADP iajs-3455 5 32 the the DET iajs-3455 5 33 theoretical theoretical ADJ iajs-3455 5 34 nuclear nuclear ADJ iajs-3455 5 35 calculation calculation NOUN iajs-3455 5 36 , , PUNCT iajs-3455 5 37 and and CCONJ iajs-3455 5 38 it it PRON iajs-3455 5 39 is be AUX iajs-3455 5 40 considered consider VERB iajs-3455 5 41 a a DET iajs-3455 5 42 key key NOUN iajs-3455 5 43 of of ADP iajs-3455 5 44 many many ADJ iajs-3455 5 45 theoretical theoretical ADJ iajs-3455 5 46 studies study NOUN iajs-3455 5 47 , , PUNCT iajs-3455 5 48 therefore therefore ADV iajs-3455 5 49 , , PUNCT iajs-3455 5 50 the the DET iajs-3455 5 51 level level NOUN iajs-3455 5 52 density density NOUN iajs-3455 5 53 in in ADP iajs-3455 5 54 pre pre ADJ iajs-3455 5 55 - - ADJ iajs-3455 5 56 equilibrium equilibrium ADJ iajs-3455 5 57 reaction reaction NOUN iajs-3455 5 58 or or CCONJ iajs-3455 5 59 what what PRON iajs-3455 5 60 is be AUX iajs-3455 5 61 the the DET iajs-3455 5 62 so so ADV iajs-3455 5 63 - - PUNCT iajs-3455 5 64 called call VERB iajs-3455 5 65 accurate accurate ADJ iajs-3455 5 66 partial partial ADJ iajs-3455 5 67 level level NOUN iajs-3455 5 68 density density NOUN iajs-3455 5 69 pld pld NOUN iajs-3455 5 70 has have AUX iajs-3455 5 71 been be AUX iajs-3455 5 72 studied study VERB iajs-3455 5 73 . . PUNCT iajs-3455 6 1 the the DET iajs-3455 6 2 partial partial ADJ iajs-3455 6 3 level level NOUN iajs-3455 6 4 density density NOUN iajs-3455 6 5 pld pld NOUN iajs-3455 6 6 used use VERB iajs-3455 6 7 in in ADP iajs-3455 6 8 pre pre ADJ iajs-3455 6 9 - - ADJ iajs-3455 6 10 equilibrium equilibrium ADJ iajs-3455 6 11 reactions reaction NOUN iajs-3455 6 12 is be AUX iajs-3455 6 13 dependent dependent ADJ iajs-3455 6 14 on on ADP iajs-3455 6 15 the the DET iajs-3455 6 16 parameter parameter NOUN iajs-3455 6 17 called call VERB iajs-3455 6 18 single single ADJ iajs-3455 6 19 particle particle NOUN iajs-3455 6 20 level level NOUN iajs-3455 6 21 density density NOUN iajs-3455 6 22 which which PRON iajs-3455 6 23 can can AUX iajs-3455 6 24 be be AUX iajs-3455 6 25 calculated calculate VERB iajs-3455 6 26 by by ADP iajs-3455 6 27 two two NUM iajs-3455 6 28 methods method NOUN iajs-3455 6 29 either either CCONJ iajs-3455 6 30 using use VERB iajs-3455 6 31 the the DET iajs-3455 6 32 equidistant equidistant ADJ iajs-3455 6 33 spacing space VERB iajs-3455 6 34 model model NOUN iajs-3455 6 35 ( ( PUNCT iajs-3455 6 36 esm esm PROPN iajs-3455 6 37 ) ) PUNCT iajs-3455 6 38 or or CCONJ iajs-3455 6 39 non non ADJ iajs-3455 6 40 - - ADJ iajs-3455 6 41 equidistant equidistant ADJ iajs-3455 6 42 spacing space VERB iajs-3455 6 43 model model NOUN iajs-3455 6 44 ( ( PUNCT iajs-3455 6 45 nonesm nonesm NOUN iajs-3455 6 46 ) ) PUNCT iajs-3455 6 47 in in ADP iajs-3455 6 48 this this DET iajs-3455 6 49 study study NOUN iajs-3455 6 50 , , PUNCT iajs-3455 6 51 the the DET iajs-3455 6 52 parameter parameter NOUN iajs-3455 6 53 𝑔 𝑔 PROPN iajs-3455 6 54 is be AUX iajs-3455 6 55 estimated estimate VERB iajs-3455 6 56 by by ADP iajs-3455 6 57 using use VERB iajs-3455 6 58 the the DET iajs-3455 6 59 relation relation NOUN iajs-3455 6 60 between between ADP iajs-3455 6 61 the the DET iajs-3455 6 62 level level NOUN iajs-3455 6 63 density density NOUN iajs-3455 6 64 parameter parameter NOUN iajs-3455 6 65 𝑔 𝑔 PROPN iajs-3455 6 66 and and CCONJ iajs-3455 6 67 π‘Ž π‘Ž PROPN iajs-3455 6 68 based base VERB iajs-3455 6 69 on on ADP iajs-3455 6 70 ericson ericson PROPN iajs-3455 6 71 and and CCONJ iajs-3455 6 72 williams williams PROPN iajs-3455 6 73 's 's PART iajs-3455 6 74 formulas formula NOUN iajs-3455 6 75 ( ( PUNCT iajs-3455 6 76 π‘Ž π‘Ž NOUN iajs-3455 6 77 = = ADJ iajs-3455 6 78 πœ‹2 πœ‹2 PROPN iajs-3455 6 79 6 6 NUM iajs-3455 6 80 𝑔 𝑔 PROPN iajs-3455 6 81 ) ) PUNCT iajs-3455 6 82 is be AUX iajs-3455 6 83 substituted substitute VERB iajs-3455 6 84 from from ADP iajs-3455 6 85 the the DET iajs-3455 6 86 thomas thomas PROPN iajs-3455 6 87 - - PUNCT iajs-3455 6 88 fermi fermi NOUN iajs-3455 6 89 formula formula NOUN iajs-3455 6 90 and and CCONJ iajs-3455 6 91 the the DET iajs-3455 6 92 new new ADJ iajs-3455 6 93 𝑔 𝑔 PROPN iajs-3455 6 94 was be AUX iajs-3455 6 95 substituted substitute VERB iajs-3455 6 96 one one NUM iajs-3455 6 97 - - PUNCT iajs-3455 6 98 component component NOUN iajs-3455 6 99 ericson ericson PROPN iajs-3455 6 100 's 's PART iajs-3455 6 101 formula formula NOUN iajs-3455 6 102 , , PUNCT iajs-3455 6 103 two two NUM iajs-3455 6 104 - - PUNCT iajs-3455 6 105 components component NOUN iajs-3455 6 106 ericson ericson PROPN iajs-3455 6 107 's 's PART iajs-3455 6 108 formula formula NOUN iajs-3455 6 109 , , PUNCT iajs-3455 6 110 williams williams PROPN iajs-3455 6 111 's 's PART iajs-3455 6 112 formula formula NOUN iajs-3455 6 113 , , PUNCT iajs-3455 6 114 spin spin VERB iajs-3455 6 115 formula formula NOUN iajs-3455 6 116 , , PUNCT iajs-3455 6 117 and and CCONJ iajs-3455 6 118 surface surface NOUN iajs-3455 6 119 formula formula NOUN iajs-3455 6 120 . . 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PUNCT iajs-3455 10 1 it it PRON iajs-3455 10 2 is be AUX iajs-3455 10 3 also also ADV iajs-3455 10 4 important important ADJ iajs-3455 10 5 for for ADP iajs-3455 10 6 medical medical ADJ iajs-3455 10 7 physics physics NOUN iajs-3455 10 8 and and CCONJ iajs-3455 10 9 nuclear nuclear ADJ iajs-3455 10 10 reaction reaction NOUN iajs-3455 10 11 design design NOUN iajs-3455 10 12 [ [ X iajs-3455 10 13 1 1 NUM iajs-3455 10 14 , , PUNCT iajs-3455 10 15 2 2 NUM iajs-3455 10 16 ] ] PUNCT iajs-3455 10 17 . . PUNCT iajs-3455 11 1 the the DET iajs-3455 11 2 first first ADJ iajs-3455 11 3 use use NOUN iajs-3455 11 4 of of ADP iajs-3455 11 5 the the DET iajs-3455 11 6 l.d l.d PROPN iajs-3455 11 7 . . 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PUNCT iajs-3455 18 1 2024 2024 NUM iajs-3455 18 2 , , PUNCT iajs-3455 18 3 37 37 NUM iajs-3455 18 4 ( ( PUNCT iajs-3455 18 5 4 4 NUM iajs-3455 18 6 ) ) PUNCT iajs-3455 18 7 155 155 NUM iajs-3455 18 8 rotational rotational ADJ iajs-3455 18 9 ground ground NOUN iajs-3455 18 10 state state NOUN iajs-3455 18 11 modes mode NOUN iajs-3455 18 12 at at ADP iajs-3455 18 13 neutron neutron NOUN iajs-3455 18 14 binding bind VERB iajs-3455 18 15 energy energy NOUN iajs-3455 18 16 . . PUNCT iajs-3455 19 1 we we PRON iajs-3455 19 2 obtained obtain VERB iajs-3455 19 3 these these DET iajs-3455 19 4 modes mode NOUN iajs-3455 19 5 using use VERB iajs-3455 19 6 both both CCONJ iajs-3455 19 7 esm esm PROPN iajs-3455 19 8 and and CCONJ iajs-3455 19 9 non non ADJ iajs-3455 19 10 - - ADJ iajs-3455 19 11 esm esm ADJ iajs-3455 19 12 for for ADP iajs-3455 19 13 each each DET iajs-3455 19 14 isotope isotope NOUN iajs-3455 19 15 , , PUNCT iajs-3455 19 16 and and CCONJ iajs-3455 19 17 we we PRON iajs-3455 19 18 compared compare VERB iajs-3455 19 19 them they PRON iajs-3455 19 20 with with ADP iajs-3455 19 21 other other ADJ iajs-3455 19 22 models model NOUN iajs-3455 19 23 and and CCONJ iajs-3455 19 24 experimental experimental ADJ iajs-3455 19 25 data datum NOUN iajs-3455 20 1 [ [ X iajs-3455 20 2 7 7 NUM iajs-3455 20 3 ] ] PUNCT iajs-3455 20 4 . . PUNCT iajs-3455 21 1 we we PRON iajs-3455 21 2 also also ADV iajs-3455 21 3 studied study VERB iajs-3455 21 4 the the DET iajs-3455 21 5 effect effect NOUN iajs-3455 21 6 of of ADP iajs-3455 21 7 the the DET iajs-3455 21 8 deformation deformation NOUN iajs-3455 21 9 parameter parameter NOUN iajs-3455 21 10 on on ADP iajs-3455 21 11 the the DET iajs-3455 21 12 nuclear nuclear ADJ iajs-3455 21 13 level level NOUN iajs-3455 21 14 density density NOUN iajs-3455 21 15 parameter parameter NOUN iajs-3455 21 16 for for ADP iajs-3455 21 17 certain certain ADJ iajs-3455 21 18 radioisotopes radioisotope NOUN iajs-3455 21 19 ( ( PUNCT iajs-3455 21 20 dy dy X iajs-3455 21 21 , , PUNCT iajs-3455 21 22 w w PROPN iajs-3455 21 23 , , PUNCT iajs-3455 21 24 and and CCONJ iajs-3455 21 25 os os NOUN iajs-3455 21 26 ) ) PUNCT iajs-3455 21 27 , , PUNCT iajs-3455 21 28 focusing focus VERB iajs-3455 21 29 on on ADP iajs-3455 21 30 level level NOUN iajs-3455 21 31 density density NOUN iajs-3455 21 32 values value NOUN iajs-3455 21 33 that that PRON iajs-3455 21 34 correspond correspond VERB iajs-3455 21 35 to to ADP iajs-3455 21 36 energies energy NOUN iajs-3455 21 37 from from ADP iajs-3455 21 38 the the DET iajs-3455 21 39 observed observe VERB iajs-3455 21 40 spectra spectra NOUN iajs-3455 21 41 near near ADP iajs-3455 21 42 the the DET iajs-3455 21 43 neutron neutron NOUN iajs-3455 21 44 binding bind VERB iajs-3455 21 45 energy energy NOUN iajs-3455 21 46 . . PUNCT iajs-3455 22 1 the the DET iajs-3455 22 2 calculations calculation NOUN iajs-3455 22 3 were be AUX iajs-3455 22 4 done do VERB iajs-3455 22 5 in in ADP iajs-3455 22 6 the the DET iajs-3455 22 7 framework framework NOUN iajs-3455 22 8 of of ADP iajs-3455 22 9 esm esm PROPN iajs-3455 22 10 , , PUNCT iajs-3455 22 11 and and CCONJ iajs-3455 22 12 the the DET iajs-3455 22 13 results result NOUN iajs-3455 22 14 have have VERB iajs-3455 22 15 good good ADJ iajs-3455 22 16 agreement agreement NOUN iajs-3455 22 17 when when SCONJ iajs-3455 22 18 they they PRON iajs-3455 22 19 are be AUX iajs-3455 22 20 compared compare VERB iajs-3455 22 21 with with ADP iajs-3455 22 22 the the DET iajs-3455 22 23 s s NOUN iajs-3455 22 24 - - PUNCT iajs-3455 22 25 wave wave NOUN iajs-3455 22 26 neutron neutron NOUN iajs-3455 22 27 resonance resonance NOUN iajs-3455 22 28 data datum NOUN iajs-3455 22 29 [ [ X iajs-3455 22 30 8 8 NUM iajs-3455 22 31 ] ] PUNCT iajs-3455 22 32 . . PUNCT iajs-3455 23 1 in in ADP iajs-3455 23 2 this this DET iajs-3455 23 3 paper paper NOUN iajs-3455 23 4 , , PUNCT iajs-3455 23 5 a a DET iajs-3455 23 6 new new ADJ iajs-3455 23 7 formula formula NOUN iajs-3455 23 8 for for ADP iajs-3455 23 9 the the DET iajs-3455 23 10 parameter parameter NOUN iajs-3455 23 11 g g PROPN iajs-3455 23 12 is be AUX iajs-3455 23 13 derived derive VERB iajs-3455 23 14 using use VERB iajs-3455 23 15 the the DET iajs-3455 23 16 relation relation NOUN iajs-3455 23 17 between between ADP iajs-3455 23 18 g g PROPN iajs-3455 23 19 and and CCONJ iajs-3455 23 20 the the DET iajs-3455 23 21 level level NOUN iajs-3455 23 22 density density NOUN iajs-3455 23 23 parameter parameter NOUN iajs-3455 24 1 a a PRON iajs-3455 24 2 ( ( PUNCT iajs-3455 24 3 a= a= ADJ iajs-3455 24 4 Ο€^2/6 Ο€^2/6 NUM iajs-3455 24 5 g g NOUN iajs-3455 24 6 ) ) PUNCT iajs-3455 25 1 [ [ X iajs-3455 25 2 9 9 NUM iajs-3455 25 3 ] ] PUNCT iajs-3455 25 4 . . PUNCT iajs-3455 26 1 the the DET iajs-3455 26 2 study study NOUN iajs-3455 26 3 aims aim VERB iajs-3455 26 4 to to PART iajs-3455 26 5 use use VERB iajs-3455 26 6 the the DET iajs-3455 26 7 new new ADJ iajs-3455 26 8 formula formula NOUN iajs-3455 26 9 g g NOUN iajs-3455 26 10 in in ADP iajs-3455 26 11 the the DET iajs-3455 26 12 calculation calculation NOUN iajs-3455 26 13 of of ADP iajs-3455 26 14 pld pld NOUN iajs-3455 26 15 in in ADP iajs-3455 26 16 a a DET iajs-3455 26 17 pre pre ADJ iajs-3455 26 18 - - ADJ iajs-3455 26 19 equilibrium equilibrium ADJ iajs-3455 26 20 region region NOUN iajs-3455 26 21 , , PUNCT iajs-3455 26 22 and and CCONJ iajs-3455 26 23 then then ADV iajs-3455 26 24 compare compare VERB iajs-3455 26 25 the the DET iajs-3455 26 26 results result NOUN iajs-3455 26 27 with with ADP iajs-3455 26 28 the the DET iajs-3455 26 29 experimental experimental ADJ iajs-3455 26 30 values value NOUN iajs-3455 26 31 of of ADP iajs-3455 26 32 pld pld NOUN iajs-3455 26 33 to to PART iajs-3455 26 34 test test VERB iajs-3455 26 35 the the DET iajs-3455 26 36 validity validity NOUN iajs-3455 26 37 of of ADP iajs-3455 26 38 the the DET iajs-3455 26 39 new new ADJ iajs-3455 26 40 formula formula NOUN iajs-3455 26 41 . . PUNCT iajs-3455 27 1 2 2 X iajs-3455 27 2 . . X iajs-3455 27 3 materials material NOUN iajs-3455 27 4 and and CCONJ iajs-3455 27 5 methods method NOUN iajs-3455 27 6 ericson ericson PROPN iajs-3455 27 7 's 's PART iajs-3455 27 8 formula formula NOUN iajs-3455 27 9 and and CCONJ iajs-3455 27 10 several several ADJ iajs-3455 27 11 corrected correct VERB iajs-3455 27 12 formulas formula NOUN iajs-3455 27 13 give give VERB iajs-3455 27 14 the the DET iajs-3455 27 15 level level NOUN iajs-3455 27 16 density density NOUN iajs-3455 27 17 in in ADP iajs-3455 27 18 the the DET iajs-3455 27 19 preequilibrium preequilibrium NOUN iajs-3455 27 20 region region NOUN iajs-3455 27 21 of of ADP iajs-3455 27 22 nuclear nuclear ADJ iajs-3455 27 23 reactions reaction NOUN iajs-3455 27 24 [ [ X iajs-3455 27 25 10 10 NUM iajs-3455 27 26 ] ] PUNCT iajs-3455 27 27 . . PUNCT iajs-3455 28 1 a a DET iajs-3455 28 2 more more ADV iajs-3455 28 3 accurate accurate ADJ iajs-3455 28 4 expression expression NOUN iajs-3455 28 5 refers refer VERB iajs-3455 28 6 to to ADP iajs-3455 28 7 the the DET iajs-3455 28 8 level level NOUN iajs-3455 28 9 density density NOUN iajs-3455 28 10 in in ADP iajs-3455 28 11 the the DET iajs-3455 28 12 pre pre ADJ iajs-3455 28 13 - - ADJ iajs-3455 28 14 equilibrium equilibrium ADJ iajs-3455 28 15 region region NOUN iajs-3455 28 16 as as ADP iajs-3455 28 17 partial partial ADJ iajs-3455 28 18 level level NOUN iajs-3455 28 19 density density NOUN iajs-3455 28 20 ( ( PUNCT iajs-3455 28 21 pld pld NOUN iajs-3455 28 22 ) ) PUNCT iajs-3455 28 23 , , PUNCT iajs-3455 28 24 as as SCONJ iajs-3455 28 25 it it PRON iajs-3455 28 26 excites excite VERB iajs-3455 28 27 some some DET iajs-3455 28 28 nucleons nucleon NOUN iajs-3455 28 29 in in ADP iajs-3455 28 30 the the DET iajs-3455 28 31 nucleus nucleus NOUN iajs-3455 28 32 when when SCONJ iajs-3455 28 33 protons proton NOUN iajs-3455 28 34 and and CCONJ iajs-3455 28 35 neutrons neutron NOUN iajs-3455 28 36 are be AUX iajs-3455 28 37 considered consider VERB iajs-3455 28 38 indistinguishable indistinguishable ADJ iajs-3455 28 39 particles particle NOUN iajs-3455 28 40 [ [ X iajs-3455 28 41 10 10 NUM iajs-3455 28 42 ] ] PUNCT iajs-3455 28 43 . . PUNCT iajs-3455 29 1 πœ”1(𝑛 πœ”1(𝑛 PROPN iajs-3455 29 2 , , PUNCT iajs-3455 29 3 𝐸 𝐸 PROPN iajs-3455 29 4 ) ) PUNCT iajs-3455 29 5 = = PUNCT iajs-3455 29 6 π‘”π‘›πΈπ‘›βˆ’1 π‘”π‘›πΈπ‘›βˆ’1 NOUN iajs-3455 30 1 𝑝!β„Ž!(π‘›βˆ’1 𝑝!β„Ž!(π‘›βˆ’1 NOUN iajs-3455 30 2 ) ) PUNCT iajs-3455 30 3 ! ! PUNCT iajs-3455 31 1 ( ( PUNCT iajs-3455 31 2 1 1 X iajs-3455 31 3 ) ) PUNCT iajs-3455 31 4 the the DET iajs-3455 31 5 symbols symbol NOUN iajs-3455 31 6 Ο‰1(n Ο‰1(n ADP iajs-3455 31 7 , , PUNCT iajs-3455 31 8 e e NOUN iajs-3455 31 9 ) ) PUNCT iajs-3455 31 10 are be AUX iajs-3455 31 11 the the DET iajs-3455 31 12 pld pld NOUN iajs-3455 31 13 , , PUNCT iajs-3455 31 14 𝐸 𝐸 PROPN iajs-3455 31 15 excitation excitation NOUN iajs-3455 31 16 energy energy NOUN iajs-3455 31 17 , , PUNCT iajs-3455 31 18 𝑝 𝑝 NOUN iajs-3455 31 19 particle particle NOUN iajs-3455 31 20 number,β„Ž number,β„Ž NUM iajs-3455 31 21 hole hole NOUN iajs-3455 31 22 number number NOUN iajs-3455 31 23 and and CCONJ iajs-3455 31 24 𝑛 𝑛 NOUN iajs-3455 31 25 = = SYM iajs-3455 31 26 𝑝 𝑝 PROPN iajs-3455 32 1 + + NUM iajs-3455 32 2 β„Ž β„Ž PROPN iajs-3455 32 3 is be AUX iajs-3455 32 4 the the DET iajs-3455 32 5 exciton exciton NOUN iajs-3455 32 6 number number NOUN iajs-3455 32 7 , , PUNCT iajs-3455 32 8 which which PRON iajs-3455 32 9 represents represent VERB iajs-3455 32 10 the the DET iajs-3455 32 11 sum sum NOUN iajs-3455 32 12 of of ADP iajs-3455 32 13 the the DET iajs-3455 32 14 particle particle NOUN iajs-3455 32 15 number number NOUN iajs-3455 32 16 and and CCONJ iajs-3455 32 17 the the DET iajs-3455 32 18 hole hole NOUN iajs-3455 32 19 number number NOUN iajs-3455 32 20 . . PUNCT iajs-3455 33 1 the the DET iajs-3455 33 2 parameter parameter NOUN iajs-3455 33 3 𝑔 𝑔 PROPN iajs-3455 33 4 is be AUX iajs-3455 33 5 the the DET iajs-3455 33 6 single single ADJ iajs-3455 33 7 particle particle NOUN iajs-3455 33 8 level level NOUN iajs-3455 33 9 density density NOUN iajs-3455 33 10 we we PRON iajs-3455 33 11 will will AUX iajs-3455 33 12 discuss discuss VERB iajs-3455 33 13 it it PRON iajs-3455 33 14 in in ADP iajs-3455 33 15 detail detail NOUN iajs-3455 33 16 later later ADV iajs-3455 33 17 . . PUNCT iajs-3455 34 1 if if SCONJ iajs-3455 34 2 the the DET iajs-3455 34 3 protons proton NOUN iajs-3455 34 4 and and CCONJ iajs-3455 34 5 the the DET iajs-3455 34 6 neutrons neutron NOUN iajs-3455 34 7 are be AUX iajs-3455 34 8 considered consider VERB iajs-3455 34 9 as as ADP iajs-3455 34 10 distinguishable distinguishable ADJ iajs-3455 34 11 particles particle NOUN iajs-3455 34 12 , , PUNCT iajs-3455 34 13 the the DET iajs-3455 34 14 pld pld NOUN iajs-3455 34 15 is be AUX iajs-3455 34 16 given give VERB iajs-3455 34 17 by by ADP iajs-3455 34 18 two two NUM iajs-3455 34 19 - - PUNCT iajs-3455 34 20 component component NOUN iajs-3455 34 21 ericson ericson PROPN iajs-3455 34 22 ’s ’s PART iajs-3455 34 23 formula formula NOUN iajs-3455 34 24 [ [ X iajs-3455 34 25 6 6 NUM iajs-3455 34 26 ] ] PUNCT iajs-3455 34 27 . . PUNCT iajs-3455 35 1 πœ”2(n πœ”2(n VERB iajs-3455 35 2 , , PUNCT iajs-3455 35 3 e e NOUN iajs-3455 35 4 ) ) PUNCT iajs-3455 35 5 = = SYM iajs-3455 35 6 ( ( PUNCT iajs-3455 35 7 π‘”πœ‹)π‘›πœ‹ π‘”πœ‹)π‘›πœ‹ X iajs-3455 35 8 ( ( PUNCT iajs-3455 35 9 π‘”πœ)π‘›πœπΈπ‘›βˆ’1 π‘”πœ)π‘›πœπΈπ‘›βˆ’1 NUM iajs-3455 35 10 π‘πœ‹!β„Žπœ‹!π‘πœ!β„Žπœ!(π‘›βˆ’1 π‘πœ‹!β„Žπœ‹!π‘πœ!β„Žπœ!(π‘›βˆ’1 NOUN iajs-3455 35 11 ) ) PUNCT iajs-3455 35 12 ! ! PUNCT iajs-3455 36 1 ( ( PUNCT iajs-3455 36 2 2 2 X iajs-3455 36 3 ) ) PUNCT iajs-3455 36 4 π‘πœ‹ π‘πœ‹ ADP iajs-3455 36 5 the the DET iajs-3455 36 6 proton proton NOUN iajs-3455 36 7 particles particle NOUN iajs-3455 36 8 , , PUNCT iajs-3455 36 9 hΟ€ hΟ€ PROPN iajs-3455 36 10 is be AUX iajs-3455 36 11 the the DET iajs-3455 36 12 proton proton NOUN iajs-3455 36 13 holes hole NOUN iajs-3455 36 14 , , PUNCT iajs-3455 36 15 p𝜐 p𝜐 PROPN iajs-3455 36 16 is be AUX iajs-3455 36 17 the the DET iajs-3455 36 18 neutron neutron NOUN iajs-3455 36 19 particles particle NOUN iajs-3455 36 20 , , PUNCT iajs-3455 36 21 h𝜐 h𝜐 PROPN iajs-3455 36 22 is be AUX iajs-3455 36 23 the the DET iajs-3455 36 24 neutron neutron NOUN iajs-3455 36 25 holes hole NOUN iajs-3455 36 26 , , PUNCT iajs-3455 36 27 nΟ€ nΟ€ NOUN iajs-3455 36 28 is be AUX iajs-3455 36 29 the the DET iajs-3455 36 30 proton proton NOUN iajs-3455 36 31 exciton exciton NOUN iajs-3455 36 32 numbers number NOUN iajs-3455 36 33 and and CCONJ iajs-3455 36 34 nΟ… nΟ… NOUN iajs-3455 36 35 is be AUX iajs-3455 36 36 the the DET iajs-3455 36 37 neutrons neutron NOUN iajs-3455 36 38 exciton exciton NOUN iajs-3455 36 39 number number NOUN iajs-3455 36 40 . . PUNCT iajs-3455 37 1 the the DET iajs-3455 37 2 symbols symbols PROPN iajs-3455 37 3 π‘”πœ‹ π‘”πœ‹ PROPN iajs-3455 37 4 and and CCONJ iajs-3455 37 5 gΟ… gΟ… PROPN iajs-3455 37 6 are be AUX iajs-3455 37 7 single single ADJ iajs-3455 37 8 particle particle NOUN iajs-3455 37 9 level level NOUN iajs-3455 37 10 densities density NOUN iajs-3455 37 11 for for ADP iajs-3455 37 12 protons proton NOUN iajs-3455 37 13 and and CCONJ iajs-3455 37 14 neutrons neutron NOUN iajs-3455 37 15 , , PUNCT iajs-3455 37 16 respectively respectively ADV iajs-3455 37 17 . . PUNCT iajs-3455 38 1 many many ADJ iajs-3455 38 2 corrections correction NOUN iajs-3455 38 3 were be AUX iajs-3455 38 4 added add VERB iajs-3455 38 5 to to ADP iajs-3455 38 6 the the DET iajs-3455 38 7 pld pld NOUN iajs-3455 38 8 formula formula NOUN iajs-3455 38 9 ; ; PUNCT iajs-3455 38 10 one one NUM iajs-3455 38 11 of of ADP iajs-3455 38 12 them they PRON iajs-3455 38 13 is be AUX iajs-3455 38 14 shown show VERB iajs-3455 38 15 in in ADP iajs-3455 38 16 william william PROPN iajs-3455 38 17 ’s ’s PART iajs-3455 38 18 formula formula NOUN iajs-3455 38 19 , , PUNCT iajs-3455 38 20 which which PRON iajs-3455 38 21 contains contain VERB iajs-3455 38 22 effect effect NOUN iajs-3455 38 23 1 1 NUM iajs-3455 38 24 of of ADP iajs-3455 38 25 pauli pauli PROPN iajs-3455 38 26 ’s ’s PART iajs-3455 38 27 exclusion exclusion NOUN iajs-3455 38 28 principle principle NOUN iajs-3455 38 29 in in ADP iajs-3455 38 30 william william PROPN iajs-3455 38 31 ’s ’s PART iajs-3455 38 32 formula formula NOUN iajs-3455 38 33 [ [ X iajs-3455 38 34 6 6 NUM iajs-3455 38 35 ] ] PUNCT iajs-3455 38 36 . . PUNCT iajs-3455 39 1 w1(n w1(n PROPN iajs-3455 39 2 , , PUNCT iajs-3455 39 3 e e NOUN iajs-3455 39 4 ) ) PUNCT iajs-3455 39 5 = = SYM iajs-3455 39 6 gn gn PROPN iajs-3455 39 7 ( ( PUNCT iajs-3455 39 8 eβˆ’a(p eβˆ’a(p ADJ iajs-3455 39 9 , , PUNCT iajs-3455 39 10 h h NOUN iajs-3455 39 11 ) ) PUNCT iajs-3455 39 12 ) ) PUNCT iajs-3455 40 1 nβˆ’1 nβˆ’1 PROPN iajs-3455 40 2 p!h!(nβˆ’1 p!h!(nβˆ’1 NOUN iajs-3455 40 3 ) ) PUNCT iajs-3455 40 4 ! ! PUNCT iajs-3455 41 1 ( ( PUNCT iajs-3455 41 2 3 3 X iajs-3455 41 3 ) ) PUNCT iajs-3455 41 4 𝐴(𝑝,β„Ž 𝐴(𝑝,β„Ž PUNCT iajs-3455 41 5 ) ) PUNCT iajs-3455 41 6 = = SYM iajs-3455 41 7 𝑝(𝑝+1)+β„Ž(β„Žβˆ’3 𝑝(𝑝+1)+β„Ž(β„Žβˆ’3 PROPN iajs-3455 41 8 ) ) PUNCT iajs-3455 41 9 2𝑔 2𝑔 NOUN iajs-3455 41 10 ( ( PUNCT iajs-3455 41 11 4 4 NUM iajs-3455 41 12 ) ) PUNCT iajs-3455 41 13 the the DET iajs-3455 41 14 second second ADJ iajs-3455 41 15 correction correction NOUN iajs-3455 41 16 is be AUX iajs-3455 41 17 the the DET iajs-3455 41 18 spin spin NOUN iajs-3455 41 19 correction correction NOUN iajs-3455 41 20 which which PRON iajs-3455 41 21 means mean VERB iajs-3455 41 22 adding add VERB iajs-3455 41 23 the the DET iajs-3455 41 24 spin spin NOUN iajs-3455 41 25 effect effect NOUN iajs-3455 41 26 to to ADP iajs-3455 41 27 the the DET iajs-3455 41 28 pld pld NOUN iajs-3455 41 29 formula formula NOUN iajs-3455 41 30 that that PRON iajs-3455 41 31 is be AUX iajs-3455 41 32 represented represent VERB iajs-3455 41 33 by by ADP iajs-3455 41 34 the the DET iajs-3455 41 35 factor factor NOUN iajs-3455 41 36 𝑅(𝐽 𝑅(𝐽 ADV iajs-3455 41 37 ) ) PUNCT iajs-3455 41 38 , , PUNCT iajs-3455 41 39 then then ADV iajs-3455 41 40 the the DET iajs-3455 41 41 pld pld NOUN iajs-3455 41 42 formula formula NOUN iajs-3455 41 43 becomes become VERB iajs-3455 41 44 [ [ X iajs-3455 41 45 10 10 NUM iajs-3455 41 46 ] ] PUNCT iajs-3455 41 47 . . PUNCT iajs-3455 42 1 π‘Š1(𝑛,𝐸)= π‘Š1(𝑛,𝐸)= NOUN iajs-3455 42 2 𝑔𝑛 𝑔𝑛 PROPN iajs-3455 42 3 πΈπ‘›βˆ’1 πΈπ‘›βˆ’1 PROPN iajs-3455 42 4 𝑝!β„Ž!(π‘›βˆ’1 𝑝!β„Ž!(π‘›βˆ’1 NOUN iajs-3455 42 5 ) ) PUNCT iajs-3455 42 6 ! ! PUNCT iajs-3455 43 1 𝑅(𝐽 𝑅(𝐽 ADV iajs-3455 43 2 ) ) PUNCT iajs-3455 43 3 ( ( PUNCT iajs-3455 43 4 5 5 X iajs-3455 43 5 ) ) PUNCT iajs-3455 43 6 𝑅(𝐽 𝑅(𝐽 ADV iajs-3455 43 7 ) ) PUNCT iajs-3455 44 1 = = PUNCT iajs-3455 45 1 2𝑗+1 2𝑗+1 NUM iajs-3455 45 2 2√2πœ‹πœŽπ‘› 2√2πœ‹πœŽπ‘› NUM iajs-3455 45 3 3 3 NUM iajs-3455 46 1 𝑒π‘₯𝑝 𝑒π‘₯𝑝 NOUN iajs-3455 47 1 [ [ X iajs-3455 47 2 βˆ’ βˆ’ X iajs-3455 47 3 ( ( PUNCT iajs-3455 47 4 𝑗+ 𝑗+ X iajs-3455 47 5 1 1 NUM iajs-3455 47 6 2 2 NUM iajs-3455 47 7 ) ) PUNCT iajs-3455 47 8 2 2 NUM iajs-3455 47 9 2πœŽπ‘› 2πœŽπ‘› NOUN iajs-3455 47 10 2 2 NUM iajs-3455 47 11 ] ] PUNCT iajs-3455 47 12 ( ( PUNCT iajs-3455 47 13 6 6 NUM iajs-3455 47 14 ) ) PUNCT iajs-3455 47 15 πœŽπ‘› πœŽπ‘› NOUN iajs-3455 47 16 is be AUX iajs-3455 47 17 the the DET iajs-3455 47 18 cut cut VERB iajs-3455 47 19 - - PUNCT iajs-3455 47 20 off off ADP iajs-3455 47 21 parameter parameter NOUN iajs-3455 47 22 , , PUNCT iajs-3455 47 23 𝐽 𝐽 PROPN iajs-3455 47 24 is be AUX iajs-3455 47 25 the the DET iajs-3455 47 26 total total ADJ iajs-3455 47 27 angular angular ADJ iajs-3455 47 28 momentum momentum NOUN iajs-3455 47 29 . . PUNCT iajs-3455 48 1 ihjpas ihjpas PROPN iajs-3455 48 2 . . PUNCT iajs-3455 49 1 2024 2024 NUM iajs-3455 49 2 , , PUNCT iajs-3455 49 3 37 37 NUM iajs-3455 49 4 ( ( PUNCT iajs-3455 49 5 4 4 NUM iajs-3455 49 6 ) ) PUNCT iajs-3455 49 7 156 156 NUM iajs-3455 49 8 the the DET iajs-3455 49 9 third third ADJ iajs-3455 49 10 correction correction NOUN iajs-3455 49 11 is be AUX iajs-3455 49 12 the the DET iajs-3455 49 13 surface surface NOUN iajs-3455 49 14 correction correction NOUN iajs-3455 49 15 , , PUNCT iajs-3455 49 16 which which PRON iajs-3455 49 17 is be AUX iajs-3455 49 18 because because SCONJ iajs-3455 49 19 the the DET iajs-3455 49 20 nuclear nuclear ADJ iajs-3455 49 21 potential potential NOUN iajs-3455 49 22 at at ADP iajs-3455 49 23 the the DET iajs-3455 49 24 surface surface NOUN iajs-3455 49 25 of of ADP iajs-3455 49 26 the the DET iajs-3455 49 27 nucleus nucleus NOUN iajs-3455 49 28 is be AUX iajs-3455 49 29 shallower shallow ADJ iajs-3455 49 30 than than SCONJ iajs-3455 49 31 it it PRON iajs-3455 49 32 is be AUX iajs-3455 49 33 inside inside ADP iajs-3455 49 34 the the DET iajs-3455 49 35 nucleus nucleus NOUN iajs-3455 50 1 [ [ X iajs-3455 50 2 6 6 NUM iajs-3455 50 3 ] ] PUNCT iajs-3455 50 4 . . PUNCT iajs-3455 51 1 πœ”1(𝑛 πœ”1(𝑛 PROPN iajs-3455 51 2 , , PUNCT iajs-3455 51 3 𝐸 𝐸 PROPN iajs-3455 51 4 , , PUNCT iajs-3455 51 5 𝑉 𝑉 PROPN iajs-3455 51 6 ) ) PUNCT iajs-3455 51 7 = = SYM iajs-3455 51 8 πœ”1(𝑛 πœ”1(𝑛 PROPN iajs-3455 51 9 , , PUNCT iajs-3455 51 10 𝐸 𝐸 PROPN iajs-3455 51 11 , , PUNCT iajs-3455 51 12 ∞ ∞ PROPN iajs-3455 51 13 ) ) PUNCT iajs-3455 51 14 Γ— Γ— PROPN iajs-3455 51 15 𝑓1(𝑛 𝑓1(𝑛 PROPN iajs-3455 51 16 , , PUNCT iajs-3455 51 17 𝐸 𝐸 PROPN iajs-3455 51 18 , , PUNCT iajs-3455 51 19 𝑉 𝑉 PROPN iajs-3455 51 20 ) ) PUNCT iajs-3455 51 21 ( ( PUNCT iajs-3455 51 22 7 7 X iajs-3455 51 23 ) ) PUNCT iajs-3455 51 24 𝑓1(𝑛 𝑓1(𝑛 PROPN iajs-3455 51 25 , , PUNCT iajs-3455 51 26 𝐸 𝐸 PROPN iajs-3455 51 27 , , PUNCT iajs-3455 51 28 𝑉 𝑉 PROPN iajs-3455 51 29 ) ) PUNCT iajs-3455 51 30 = = PUNCT iajs-3455 51 31 βˆ‘ βˆ‘ PROPN iajs-3455 51 32 ( ( PUNCT iajs-3455 51 33 βˆ’1)𝑗𝐢𝑗 βˆ’1)𝑗𝐢𝑗 PROPN iajs-3455 51 34 β„Ž β„Ž X iajs-3455 51 35 [ [ PUNCT iajs-3455 51 36 πΈβˆ’π‘—π‘‰(β„Ž πΈβˆ’π‘—π‘‰(β„Ž PROPN iajs-3455 51 37 ) ) PUNCT iajs-3455 51 38 𝐸 𝐸 PROPN iajs-3455 51 39 ] ] PUNCT iajs-3455 51 40 π‘›βˆ’1 π‘›βˆ’1 NUM iajs-3455 51 41 β„Ž β„Ž X iajs-3455 51 42 𝑗=0 𝑗=0 PROPN iajs-3455 52 1 ΞΈ ΞΈ PROPN iajs-3455 52 2 ( ( PUNCT iajs-3455 52 3 𝐸 𝐸 PROPN iajs-3455 52 4 βˆ’ βˆ’ PROPN iajs-3455 52 5 𝑗𝑉(β„Ž 𝑗𝑉(β„Ž NOUN iajs-3455 52 6 ) ) PUNCT iajs-3455 52 7 ) ) PUNCT iajs-3455 53 1 ( ( PUNCT iajs-3455 53 2 8) 8) NUM iajs-3455 53 3 the the DET iajs-3455 53 4 parameter parameter NOUN iajs-3455 53 5 𝑔 𝑔 PROPN iajs-3455 53 6 can can AUX iajs-3455 53 7 be be AUX iajs-3455 53 8 given give VERB iajs-3455 53 9 either either CCONJ iajs-3455 53 10 in in ADP iajs-3455 53 11 the the DET iajs-3455 53 12 framework framework NOUN iajs-3455 53 13 of of ADP iajs-3455 53 14 the the DET iajs-3455 53 15 equidistant equidistant ADJ iajs-3455 53 16 spacing space VERB iajs-3455 53 17 model model NOUN iajs-3455 53 18 esm esm PROPN iajs-3455 53 19 or or CCONJ iajs-3455 53 20 by by ADP iajs-3455 53 21 the the DET iajs-3455 53 22 non non ADJ iajs-3455 53 23 - - ADJ iajs-3455 53 24 equidistant equidistant ADJ iajs-3455 53 25 spacing space VERB iajs-3455 53 26 model model NOUN iajs-3455 53 27 ( ( PUNCT iajs-3455 53 28 non non ADJ iajs-3455 53 29 - - ADJ iajs-3455 53 30 esm esm ADJ iajs-3455 53 31 ) ) PUNCT iajs-3455 54 1 [ [ X iajs-3455 54 2 8 8 NUM iajs-3455 54 3 ] ] PUNCT iajs-3455 54 4 . . PUNCT iajs-3455 55 1 in in ADP iajs-3455 55 2 this this DET iajs-3455 55 3 study study NOUN iajs-3455 55 4 , , PUNCT iajs-3455 55 5 we we PRON iajs-3455 55 6 will will AUX iajs-3455 55 7 derive derive VERB iajs-3455 55 8 a a DET iajs-3455 55 9 new new ADJ iajs-3455 55 10 formula formula NOUN iajs-3455 55 11 of of ADP iajs-3455 55 12 𝑔 𝑔 NOUN iajs-3455 55 13 using use VERB iajs-3455 55 14 the the DET iajs-3455 55 15 relation relation NOUN iajs-3455 55 16 between between ADP iajs-3455 55 17 the the DET iajs-3455 55 18 level level NOUN iajs-3455 55 19 density density NOUN iajs-3455 55 20 parameter parameter NOUN iajs-3455 55 21 π‘Ž π‘Ž NOUN iajs-3455 55 22 and and CCONJ iajs-3455 55 23 𝑔 𝑔 X iajs-3455 55 24 [ [ X iajs-3455 55 25 11 11 NUM iajs-3455 55 26 , , PUNCT iajs-3455 55 27 1 1 NUM iajs-3455 55 28 ] ] PUNCT iajs-3455 55 29 . . PUNCT iajs-3455 56 1 𝑔 𝑔 PROPN iajs-3455 56 2 = = SYM iajs-3455 56 3 6 6 NUM iajs-3455 56 4 πœ‹2 πœ‹2 NOUN iajs-3455 56 5 π‘Ž π‘Ž X iajs-3455 56 6 ( ( PUNCT iajs-3455 56 7 9 9 NUM iajs-3455 56 8 ) ) PUNCT iajs-3455 56 9 the the DET iajs-3455 56 10 parameter parameter NOUN iajs-3455 56 11 a a PRON iajs-3455 56 12 from from ADP iajs-3455 56 13 the the DET iajs-3455 56 14 thomas thomas PROPN iajs-3455 56 15 - - PUNCT iajs-3455 56 16 fermi fermi NOUN iajs-3455 56 17 formula formula NOUN iajs-3455 56 18 . . PUNCT iajs-3455 57 1 π‘Ž π‘Ž X iajs-3455 57 2 = = SYM iajs-3455 57 3 ( ( PUNCT iajs-3455 57 4 0.109(1 0.109(1 NUM iajs-3455 57 5 βˆ’ βˆ’ PROPN iajs-3455 57 6 4.476𝐼2)𝐴 4.476𝐼2)𝐴 NOUN iajs-3455 57 7 + + CCONJ iajs-3455 57 8 0.076(1 0.076(1 NOUN iajs-3455 58 1 + + CCONJ iajs-3455 58 2 31.47𝐼2)𝐴 31.47𝐼2)𝐴 PROPN iajs-3455 58 3 2 2 NUM iajs-3455 58 4 3⁄ 3⁄ NUM iajs-3455 58 5 βˆ’ βˆ’ NOUN iajs-3455 58 6 0.0024𝑍2𝐴 0.0024𝑍2𝐴 NOUN iajs-3455 58 7 βˆ’1 βˆ’1 NOUN iajs-3455 58 8 3⁄ 3⁄ NUM iajs-3455 58 9 ) ) PUNCT iajs-3455 58 10 ( ( PUNCT iajs-3455 58 11 10 10 NUM iajs-3455 58 12 ) ) PUNCT iajs-3455 58 13 𝐼 𝐼 NOUN iajs-3455 58 14 represents represent VERB iajs-3455 58 15 isospin isospin NOUN iajs-3455 58 16 , , PUNCT iajs-3455 58 17 𝑍 𝑍 PROPN iajs-3455 58 18 is be AUX iajs-3455 58 19 the the DET iajs-3455 58 20 atomic atomic ADJ iajs-3455 58 21 number number NOUN iajs-3455 58 22 , , PUNCT iajs-3455 58 23 𝐴 𝐴 PROPN iajs-3455 58 24 is be AUX iajs-3455 58 25 the the DET iajs-3455 58 26 mass mass ADJ iajs-3455 58 27 number number NOUN iajs-3455 58 28 then then ADV iajs-3455 58 29 , , PUNCT iajs-3455 58 30 𝑔 𝑔 X iajs-3455 58 31 become become VERB iajs-3455 58 32 𝑔 𝑔 PROPN iajs-3455 58 33 = = SYM iajs-3455 58 34 6 6 NUM iajs-3455 58 35 πœ‹2 πœ‹2 NOUN iajs-3455 58 36 ( ( PUNCT iajs-3455 58 37 0.068𝐴 0.068𝐴 X iajs-3455 58 38 + + CCONJ iajs-3455 58 39 0.213𝐴 0.213𝐴 NUM iajs-3455 58 40 2 2 NUM iajs-3455 58 41 3⁄ 3⁄ NUM iajs-3455 58 42 + + NUM iajs-3455 58 43 0.385𝐴 0.385𝐴 NUM iajs-3455 58 44 1 1 NUM iajs-3455 58 45 3⁄ 3⁄ NUM iajs-3455 58 46 ) ) PUNCT iajs-3455 58 47 ( ( PUNCT iajs-3455 58 48 11 11 NUM iajs-3455 58 49 ) ) PUNCT iajs-3455 58 50 in in ADP iajs-3455 58 51 the the DET iajs-3455 58 52 case case NOUN iajs-3455 58 53 of of ADP iajs-3455 58 54 two two NUM iajs-3455 58 55 - - PUNCT iajs-3455 58 56 component component NOUN iajs-3455 58 57 [ [ X iajs-3455 58 58 6 6 NUM iajs-3455 58 59 ] ] X iajs-3455 58 60 : : PUNCT iajs-3455 58 61 π‘”πœ‹ π‘”πœ‹ NOUN iajs-3455 58 62 = = PUNCT iajs-3455 58 63 𝑍 𝑍 PROPN iajs-3455 58 64 𝐴 𝐴 PROPN iajs-3455 58 65 𝑔 𝑔 PROPN iajs-3455 58 66 ( ( PUNCT iajs-3455 58 67 12 12 NUM iajs-3455 58 68 ) ) PUNCT iajs-3455 58 69 π‘”πœ π‘”πœ NOUN iajs-3455 58 70 = = SYM iajs-3455 58 71 𝑁 𝑁 PROPN iajs-3455 58 72 𝐴 𝐴 PROPN iajs-3455 58 73 𝑔 𝑔 PROPN iajs-3455 58 74 ( ( PUNCT iajs-3455 58 75 13 13 NUM iajs-3455 58 76 ) ) PUNCT iajs-3455 58 77 in in ADP iajs-3455 58 78 the the DET iajs-3455 58 79 next next ADJ iajs-3455 58 80 section section NOUN iajs-3455 58 81 , , PUNCT iajs-3455 58 82 the the DET iajs-3455 58 83 g g PROPN iajs-3455 58 84 formulae formulae NOUN iajs-3455 58 85 are be AUX iajs-3455 58 86 substituted substitute VERB iajs-3455 58 87 in in ADP iajs-3455 58 88 all all DET iajs-3455 58 89 pld pld NOUN iajs-3455 58 90 formulas formula NOUN iajs-3455 58 91 and and CCONJ iajs-3455 58 92 compared compare VERB iajs-3455 58 93 to to ADP iajs-3455 58 94 the the DET iajs-3455 58 95 results result NOUN iajs-3455 58 96 with with ADP iajs-3455 58 97 the the DET iajs-3455 58 98 experimental experimental ADJ iajs-3455 58 99 data datum NOUN iajs-3455 58 100 . . PUNCT iajs-3455 59 1 3 3 X iajs-3455 59 2 . . NOUN iajs-3455 59 3 results result NOUN iajs-3455 59 4 and and CCONJ iajs-3455 59 5 discussion discussion NOUN iajs-3455 59 6 the the DET iajs-3455 59 7 discussion discussion NOUN iajs-3455 59 8 was be AUX iajs-3455 59 9 made make VERB iajs-3455 59 10 by by ADP iajs-3455 59 11 comparing compare VERB iajs-3455 59 12 the the DET iajs-3455 59 13 theoretical theoretical ADJ iajs-3455 59 14 curves curve NOUN iajs-3455 59 15 that that PRON iajs-3455 59 16 came come VERB iajs-3455 59 17 from from ADP iajs-3455 59 18 substituting substitute VERB iajs-3455 59 19 g g NOUN iajs-3455 59 20 from from ADP iajs-3455 59 21 the the DET iajs-3455 59 22 thomas thomas PROPN iajs-3455 59 23 - - PUNCT iajs-3455 59 24 fermi fermi NOUN iajs-3455 59 25 formula formula NOUN iajs-3455 59 26 in in ADP iajs-3455 59 27 all all DET iajs-3455 59 28 pld pld PRON iajs-3455 59 29 formulas formula NOUN iajs-3455 59 30 mentioned mention VERB iajs-3455 59 31 above above ADV iajs-3455 59 32 with with ADP iajs-3455 59 33 the the DET iajs-3455 59 34 experimental experimental ADJ iajs-3455 59 35 data datum NOUN iajs-3455 59 36 , , PUNCT iajs-3455 59 37 and and CCONJ iajs-3455 59 38 the the DET iajs-3455 59 39 equations equation NOUN iajs-3455 59 40 are be AUX iajs-3455 59 41 programmed program VERB iajs-3455 59 42 using use VERB iajs-3455 59 43 mat mat NOUN iajs-3455 59 44 . . PUNCT iajs-3455 59 45 lab lab PROPN iajs-3455 59 46 . . PUNCT iajs-3455 60 1 figure figure NOUN iajs-3455 60 2 1 1 NUM iajs-3455 60 3 . . PUNCT iajs-3455 60 4 shows show VERB iajs-3455 60 5 a a DET iajs-3455 60 6 comparison comparison NOUN iajs-3455 60 7 between between ADP iajs-3455 60 8 one one NUM iajs-3455 60 9 - - PUNCT iajs-3455 60 10 component component NOUN iajs-3455 60 11 ericson ericson PROPN iajs-3455 60 12 's 's PART iajs-3455 60 13 formula formula NOUN iajs-3455 60 14 of of ADP iajs-3455 60 15 the the DET iajs-3455 60 16 pld pld NOUN iajs-3455 60 17 curve curve NOUN iajs-3455 60 18 with with ADP iajs-3455 60 19 𝑔 𝑔 PROPN iajs-3455 60 20 from from ADP iajs-3455 60 21 the the DET iajs-3455 60 22 thomas thomas PROPN iajs-3455 60 23 - - PUNCT iajs-3455 60 24 fermi fermi NOUN iajs-3455 60 25 formula formula NOUN iajs-3455 60 26 and and CCONJ iajs-3455 60 27 the the DET iajs-3455 60 28 experimental experimental ADJ iajs-3455 60 29 data datum NOUN iajs-3455 60 30 . . PUNCT iajs-3455 61 1 it it PRON iajs-3455 61 2 is be AUX iajs-3455 61 3 noticed notice VERB iajs-3455 61 4 that that SCONJ iajs-3455 61 5 the the DET iajs-3455 61 6 theoretical theoretical ADJ iajs-3455 61 7 curve curve NOUN iajs-3455 61 8 is be AUX iajs-3455 61 9 less less ADJ iajs-3455 61 10 than than ADP iajs-3455 61 11 the the DET iajs-3455 61 12 experimental experimental ADJ iajs-3455 61 13 curve curve NOUN iajs-3455 61 14 up up ADP iajs-3455 61 15 to to PART iajs-3455 61 16 4 4 NUM iajs-3455 61 17 mev mev NOUN iajs-3455 61 18 and and CCONJ iajs-3455 61 19 from from ADP iajs-3455 61 20 4 4 NUM iajs-3455 61 21 mev mev NOUN iajs-3455 61 22 to to ADP iajs-3455 61 23 5 5 NUM iajs-3455 61 24 mev mev PROPN iajs-3455 61 25 . . PUNCT iajs-3455 62 1 both both DET iajs-3455 62 2 curves curve NOUN iajs-3455 62 3 become become VERB iajs-3455 62 4 in in ADP iajs-3455 62 5 agreement agreement NOUN iajs-3455 62 6 , , PUNCT iajs-3455 62 7 and and CCONJ iajs-3455 62 8 after after ADP iajs-3455 62 9 5 5 NUM iajs-3455 62 10 mev mev PROPN iajs-3455 62 11 , , PUNCT iajs-3455 62 12 the the DET iajs-3455 62 13 theoretical theoretical ADJ iajs-3455 62 14 curve curve NOUN iajs-3455 62 15 becomes become VERB iajs-3455 62 16 higher high ADJ iajs-3455 62 17 than than ADP iajs-3455 62 18 the the DET iajs-3455 62 19 experimental experimental ADJ iajs-3455 62 20 curve curve NOUN iajs-3455 62 21 . . PUNCT iajs-3455 63 1 in in ADP iajs-3455 63 2 other other ADJ iajs-3455 63 3 words word NOUN iajs-3455 63 4 , , PUNCT iajs-3455 63 5 the the DET iajs-3455 63 6 theoretical theoretical ADJ iajs-3455 63 7 curve curve NOUN iajs-3455 63 8 mediates mediate VERB iajs-3455 63 9 the the DET iajs-3455 63 10 experimental experimental ADJ iajs-3455 63 11 curve curve NOUN iajs-3455 63 12 . . PUNCT iajs-3455 64 1 in in ADP iajs-3455 64 2 other other ADJ iajs-3455 64 3 words word NOUN iajs-3455 64 4 , , PUNCT iajs-3455 64 5 the the DET iajs-3455 64 6 theoretical theoretical ADJ iajs-3455 64 7 curve curve NOUN iajs-3455 64 8 mediates mediate VERB iajs-3455 64 9 the the DET iajs-3455 64 10 experimental experimental ADJ iajs-3455 64 11 curve curve NOUN iajs-3455 64 12 . . PUNCT iajs-3455 65 1 this this DET iajs-3455 65 2 behavior behavior NOUN iajs-3455 65 3 can can AUX iajs-3455 65 4 be be AUX iajs-3455 65 5 attributed attribute VERB iajs-3455 65 6 to to ADP iajs-3455 65 7 the the DET iajs-3455 65 8 𝑔 𝑔 PROPN iajs-3455 65 9 formula formula NOUN iajs-3455 65 10 from from ADP iajs-3455 65 11 thomas thomas PROPN iajs-3455 65 12 - - PUNCT iajs-3455 65 13 fermi fermi NOUN iajs-3455 65 14 which which PRON iajs-3455 65 15 contains contain VERB iajs-3455 65 16 𝐴 𝐴 PROPN iajs-3455 65 17 with with ADP iajs-3455 65 18 different different ADJ iajs-3455 65 19 powers power NOUN iajs-3455 65 20 , , PUNCT iajs-3455 65 21 as as SCONJ iajs-3455 65 22 shown show VERB iajs-3455 65 23 in in ADP iajs-3455 65 24 equation equation NOUN iajs-3455 65 25 ( ( PUNCT iajs-3455 65 26 10 10 NUM iajs-3455 65 27 ) ) PUNCT iajs-3455 65 28 . . PUNCT iajs-3455 66 1 this this PRON iajs-3455 66 2 makes make VERB iajs-3455 66 3 the the DET iajs-3455 66 4 pld pld NOUN iajs-3455 66 5 depending depend VERB iajs-3455 66 6 on on ADP iajs-3455 66 7 𝑔 𝑔 PROPN iajs-3455 66 8 from from ADP iajs-3455 66 9 thomas thomas PROPN iajs-3455 66 10 - - PUNCT iajs-3455 66 11 fermi fermi NOUN iajs-3455 66 12 increasing increase VERB iajs-3455 66 13 moderately moderately ADV iajs-3455 66 14 in in ADP iajs-3455 66 15 agreement agreement NOUN iajs-3455 66 16 with with ADP iajs-3455 66 17 the the DET iajs-3455 66 18 experimental experimental ADJ iajs-3455 66 19 data datum NOUN iajs-3455 66 20 . . PUNCT iajs-3455 67 1 figure figure NOUN iajs-3455 67 2 2 2 NUM iajs-3455 67 3 . . PUNCT iajs-3455 67 4 shows show VERB iajs-3455 67 5 a a DET iajs-3455 67 6 comparison comparison NOUN iajs-3455 67 7 between between ADP iajs-3455 67 8 two two NUM iajs-3455 67 9 components component NOUN iajs-3455 67 10 of of ADP iajs-3455 67 11 ericson ericson PROPN iajs-3455 67 12 's 's PART iajs-3455 67 13 formula formula NOUN iajs-3455 67 14 for for ADP iajs-3455 67 15 pld pld NOUN iajs-3455 67 16 with with ADP iajs-3455 67 17 g g NOUN iajs-3455 67 18 from from ADP iajs-3455 67 19 the the DET iajs-3455 67 20 thomas thomas PROPN iajs-3455 67 21 - - PUNCT iajs-3455 67 22 fermi fermi NOUN iajs-3455 67 23 formula formula NOUN iajs-3455 67 24 and and CCONJ iajs-3455 67 25 the the DET iajs-3455 67 26 experimental experimental ADJ iajs-3455 67 27 curve curve NOUN iajs-3455 67 28 . . PUNCT iajs-3455 68 1 because because SCONJ iajs-3455 68 2 two two NUM iajs-3455 68 3 components component NOUN iajs-3455 68 4 divide divide VERB iajs-3455 68 5 ihjpas ihjpa NOUN iajs-3455 68 6 . . PUNCT iajs-3455 69 1 2024 2024 NUM iajs-3455 69 2 , , PUNCT iajs-3455 69 3 37 37 NUM iajs-3455 69 4 ( ( PUNCT iajs-3455 69 5 4 4 NUM iajs-3455 69 6 ) ) PUNCT iajs-3455 69 7 157 157 NUM iajs-3455 69 8 the the DET iajs-3455 69 9 energy energy NOUN iajs-3455 69 10 into into ADP iajs-3455 69 11 more more ADJ iajs-3455 69 12 particles particle NOUN iajs-3455 69 13 than than ADP iajs-3455 69 14 one one NUM iajs-3455 69 15 , , PUNCT iajs-3455 69 16 the the DET iajs-3455 69 17 theoretical theoretical ADJ iajs-3455 69 18 curve curve NOUN iajs-3455 69 19 lies lie VERB iajs-3455 69 20 below below ADP iajs-3455 69 21 the the DET iajs-3455 69 22 experimental experimental ADJ iajs-3455 69 23 curve curve NOUN iajs-3455 69 24 . . 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