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３次元コヒーレント共鳴励起を用いたＸ線-VUV領域の２重共鳴と磁気サブレベルコントロール（中野祐司）…

5(シリーズ) 衝突論ノート III．非弾性散乱だけが起こることはない－ 流束保存とポテンシャルの虚と実－
（島村勲）

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原子衝突研究協会第 35 回年会報告（行事委員長）…

21

原子衝突若手の会 第 31 回秋の学校開催のお知らせ（山本果林）…

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細則変更に関する会長からのお願い

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26

国際会議発表奨励事業に関するお知らせ（庶務幹事）

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4ዮᛟᲭഏΨǳȒȸȬȳȈσᯚѕឪǛဇƍƨ᳒ዴ-VUV ᪸؏ƷᲬ᣻σᯚƱᄬൢǵȖȬșȫǳȳȈȭȸȫɶ᣼ᅎӮ nakano-y@riken.jpྸ҄‫ܖ‬ᄂᆮ৑ųிҾ‫܇‬Ў‫܇‬ཋྸᄂᆮܴ
࠯঺ 22 ࠰ 8 உ 15 ଐҾᆜӖ˄ᡈ˩ƴƓƍƯλ‫ݧ‬ήƸӞχႎƳ࠯᩿ඬưƋǓᲦҾ‫܇‬ȏȟȫȈȋǢȳƴ‫ݣ‬Ƣǔԗ஖ႎƳઅѣƱƠƯ

1. ƸơǊƴ

ӕǓৢǘǕǔᲨࢼƬƯྸᛯႎƴƸᲦήǛ࢘ƯƳƘҾ‫܇‬ƳƲƷϋᢿཞ७Ǜ‫٭‬ƑǔƨǊƷ৖ඥƱƠƱǋҾ‫܇‬ƴ‫ݣ‬ƠƯ˴ǒƔƷ૾ඥư E0 exp(−ik · r)ƯᲦҾ‫܇‬ᘔᆳƴǑǔ৖ඥƱᲦήǛ̅Ə৖ඥƸᲦಮŷƷǑƏƳઅѣǛɨƑƯǍǕƹήѕឪƱӷಮƴҾƳ‫ئ‬᩿ưƠƹƠƹൔ᠋ƞǕǔᲨ‫ٶ‬ƘƷ‫ئ‬ӳᲦή‫܇‬ᢟᆆǛឪƜƢƜƱƕưƖǔƜƱƴƳǔᲨܱᨥᲦǛ̅ƏƜƱƷȡȪȃȈƸƦƷҥᑥࣱƴƋǓᲦཞƜƷǑƏƳྵᝋƸ‫׋‬Ძ (b) ƷǑƏƴᲦҾ‫܇‬ᘔᆳ७ᢠ৸ႎƳҾ‫܇‬СࣂƕӧᏡưƋǔƕᲦƦƷɟ૾ᲦƴƓƍƯ೅ႎҾ‫܇‬ƕԗ஖ႎƴɳǜưƍǔ‫ئ‬ӳƴȬȸǶȸǍ્‫ݧ‬ήƷМဇưƖǔඬᧈ᪸؏ƸᨂǒܱྵƞǕǔᲨҾ‫܇‬Ʒ᩺ഥኒƔǒᙸǕƹᲦԗ஖‫ئ‬ǕƯƍǔᲨƜǕƴ‫ݣ‬ƠᲦᘔᆳƷᢅᆉưƸಮŷƳɶǛᡫᢅƢǔƜƱƸᲦ଺᧓ႎƴԗ஖ႎƳઅѣǛ᩼࢐ࣱᢅᆉƕဃơǔƨǊᲦཎ‫ܭ‬Ʒཞ७ƷǈǁᢟӖƚǔƱƍƏॖԛưᩓᄬඬǛༀ‫ݧ‬ƞǕǔƜƱƱ

ᆆƞƤǔƱƍƏƜƱƸܾତưƳƍƕᲦᘔᆳǨȍಒࣞႎƴӷሁưƋǓᲦήԈӓƱӷಮƷவˑưσȫǮȸƱƠƯƸ meV ˌɦƔǒ TeV ˌɥƱƍƏᯚႎƴѕឪƕឪƜǔƷưƋǔᲨƜǕƕǳȒȸȬ࠼ርƳǨȍȫǮȸƕМဇӧᏡưƋǔᲨஜᆜưƸᲦȳȈσᯚѕឪƷஇǋؕஜႎƳᎋƑ૾ưƋǔᲨǋƜƷᲬƭƷ৖ඥƷМໜǛ́ƤਤƬƨ৖ඥᲦƢƳǘƪǖǜήѕឪƱƸఌஜႎƴီƳǔྵᝋưƋǓᲦƪᲦҾ‫܇‬ᘔᆳǛМဇƠƨཞ७ᢠ৸ႎƳҾ‫܇‬ཞ७Ʒ᣽‫܇‬ᛯႎƳӕǓৢƍưྵǕǔલ˩ή‫܇‬Ƹܱή‫܇‬СࣂƱƠƯᲦǳȒȸȬȳȈσᯚѕឪᲢResonantƱီƳǔЎ૝᧙̞ǛਤƪᲦǇƨ RCE ᐯ˳ƕ‫ׅ‬

Coherent Excitation: RCEᲣ[1, 2, 3, 4, 5, 6] ƴ৵ྵᝋƱƠƯƷ᩿ͨǋਤƪӳǘƤǔƳƲᲦ᣽‫܇‬Ǒǔ৖ඥǛᚐᛟƢǔᲨщ‫ܖ‬Ǎ૝ʏྵᝋƷఌஜƴᇌƪᡉǔƜƱƷưƖǔ
ᐻԛขƍȆȸȞưǋƋǔƕᲦƜǕǒƴ᧙ƠƯƸ‫׋‬Ძ (a) ƸᲦ᩺ഥƠƯƍǔҾ‫܇‬ƕήǛༀ‫ݧ‬ƞǕࢸҞưᜭᛯƢǔƜƱƱƢǔᲨƯѕឪƢǔಮ‫܇‬ǛᅆƠƯƍǔᲨƜƷƱƖᲦҞӞχ

RCE ƴǑǔᢟᆆƸᲦҾྸႎƴƸƦƷ‫ݣ‬ᝋǛᢠƹƣᲦᘔᆳ᬴ܱƷཎࣉưƋǔࠢ࠼ƍǨȍȫǮȸD ගບ㉳

᪸؏Ǜ෇ƔƠƯᲦƋǒǏǔԗඬૠ᪸؏ƷσᯚƕE ࢥࣄ࣮ࣞࣥࢺඹ㬆ບ㉳МဇưƖǔᲨྵƴᠾ߻‫ٻ‬Ʒဣ‫ޛ‬ᄂưƸȬȸǶȸගϬҲƠƨ Rb Ҿ‫܇‬ǛဇƍƯ RF ᪸؏Ʒ RCE ᬴ܱƕᘍǘǕƯƓǓ [7, 8]Ღɟ૾ưஜᄂᆮưƸьᡮ֥ǛМဇƢǔƜƱư X ዴ᪸؏ƷҾ‫܇‬ᢟᆆǛ‫ݣ‬ᝋᶆⓗཎᏊƱƠƯƍǔᲨஜᄂᆮưМဇƢǔ೅ႎƸᲦಊǊƯ‫ ׋‬1: (a) ήᲢᩓᄬඬᲣǛༀ‫ݧ‬ƞǕƯѕឪƢǔҾ‫܇‬Შ(b)ԗ஖ႎƴƳǒǜƩ೅ႎҾ‫܇‬ƕ˺ǔԗ஖ȝȆȳǷȣ
ȫɶǛᡫᢅƢǔҾ‫܇‬ᲨችࡇǑƘԗ஖ႎƴᣐፗƞǕƨҾ‫܇‬Ʒᨼ‫ׇ‬ᲦƢƳǘƪǷȪǳȳኽ୒ưƋǔᲨƜǕƴǑǓ 10−10 m5ǪȸȀȸƷԗ஖ȝȆȳǷȣȫƕМဇưƖᲦƞǒ(a)ƴήᡮᡈƘǇưьᡮƞǕƨǤǪȳƸ 108 m/s ƷᡮࡇǛਤƭƨǊᲦƦƷԗඬૠƸ 1018 Hz ƴᢋƢ

d

ධᑕ
࢖࢜ࣥ

{

ǔᲨƜǕƸ X ዴ᪸؏ƴƓƚǔ RCE ƕܱဇưƖ

v

.....

ǔƜƱǛॖԛƠᲦȬȸǶȸƷМဇƕ‫׉‬ᩊƳჺඬ

1ᯛࡢཎᏊ㠃(b)ᧈ᪸؏ƴƓƍƯҾ‫܇‬ཞ७ƷСࣂǛӧᏡƱƢǔஊ

N=1ဇƳ৖ඥƱƠƯ஖ࢳưƖǔᲨஜᆜưƸᲦǿǤȈȫƷƱƓǓᲦᄬൢǵȖȬșȫ
ƷǳȳȈȭȸȫƱᲦX ዴ-VUV ᪸؏ƷᲬ᣻σᯚƴᛅǛᨂ‫ܭ‬ƠƯؕஜƔǒЎƔǓǍƢƘᚐᛟƢǔ

N=3|S(ω)|2 / Ν2

ƱƱǋƴᲦҾ‫܇‬ᘔᆳƱƍƏᙻໜƔǒǈƨƱƖƷ

RCE ྵᝋƷஜឋǛᜭᛯƠƨƍᲨ˂Ʒ᬴ܱƳƲǋԃǊƨᲦǑǓɟᑍႎᲦѼਙႎƳϋܾƴƭƍƯƸᲦN = 10КƷᚐᛟᚡʙǛӋༀ᪬ƚǕƹ࠳ƍưƋǔ [9]ᲨƳƓᲦஜᆜƷ‫׋‬ƷƍƘƭƔƸӋᎋ૨ྂ [9, 10, 11]Ɣǒɟᢿ̲ദƠƯ᠃᠍ƠƨǋƷưƋǔᲨN = 100

2. ኽ୒‫ئ‬ƴǑǔ RCE ƷؕᄽҾྸኽ୒ϋƷԗ஖ȝȆȳǷȣȫ V (r) ƸƠƹƠƹᲦV (r) =

Vg exp (−2πig · r) ,ω(1)

‫ ׋‬2: (a) N ̾Ʒ೅ႎҾ‫܇‬ƕ˺ǔԗ஖ȝȆȳǷȣȫɶǛᡫᢅƢǔǤǪȳᲦӏƼ (b) ǤǪȳƕज़ơǔઅѣƷȕȸȪǨǹȚǯȈȫᲢࢍࡇƸ N 2 ưᙹ఍҄ᲣᲨgƱᲦȕȸȪǨኢૠƷ࢟ưᘙƞǕᲦVg ƸȕȸȪǨ̞ૠᲦg Ƹᡞ఍‫܇‬șǯȈȫưƋǔᲨƜƷɶǛǤǪȳƕᡮࡇ v ưᡫᢅƠƨƱƖƴज़ơǔਰѣᩓ‫ئ‬ưƋǔƷưᲦƜǕǛ (2) ࡸƴˊλƢǔƱᲦǛ൭ǊǔƴƸȝȆȳǷȣȫ V (r) ǛࣇЎƠᲦኽ୒F (r , t ) =Ʒ᩺ഥኒƔǒǤǪȳ᩺ഥኒƴȭȸȬȳȄ‫٭‬੭Ǜ




γ2
× exp −2πig · r +(β · r )β Ღγ+1‫ ئ‬B ƸᲦᡮࡇ v ưѣƘॹࣱኒƴƓƍƯᲦγ2β (β · F) ,
γ+1

⎛


1
γ2
B = γ B − β × F −β (β · B) ,
c
γ+1

⎛

⎞

(6)
(7)

ƕࢽǒǕᲦƜǕƕǤǪȳƕज़ơǔਰѣᩓ‫ئ‬Ʒ࢟

(3)ưƋǔᲨƨƩƠᲦॹࣱኒƴƓƚǔˮፗࡈ೅Ʊ଺ƱȭȸȬȳȄ‫٭‬੭‫٭‬੭ƞǕǔ [12]ᲨƜƜư c ƸήᡮᲦβ = v/cᲦγ = 1/ 1 − |β|2 ưƋǔᲨƍǇᲦ᧓ƷȭȸȬȳȄ‫٭‬੭Ღct = γ(ct − β · r),(8)2γr = r +(β · r)β − γβct, (9)γ+1ኽ୒Ʒ᩺ഥኒƴƓƍƯᄬ‫ئ‬ƸƳƘᲦ
F(r) = −∇V (r)=
2πigVg exp (−2πig · r) , (4)g

B(r) = 0,⎞2πVg γgx
Fgx
⎟
⎟ ⎜
⎜
⎟
⎟ ⎜
Fg = ⎜⎝ Fgy ⎠ = ⎝ 2πVg γgy ⎠ ,2πVg gz
Fgz

(2)



Fg exp[−2πiγg · vt ]gƢǕƹǑƍᲨཎഷႻ‫ݣ‬ᛯƴǑǕƹᲦᩓ‫ ئ‬FᲦᄬ
F = γ (F + cβ × B) −ǛဇƍƨᲨ ǤǪȳƷ᩺ഥኒưƸࡸ (3) Ʒਰѣ(5)ᄬ‫ئ‬ǋྵǕǔƕᲦƜǕƸᩓ‫ئ‬ƴൔǂƯҗЎ‫ݱ‬ƞ6ƍƷư໯ᙻưƖǔᲨȕȸȪǨ̞ૠ Fg ƕਰѣᩓ

(a)

[110]

‫ئ‬ƷਰࠢșǯȈȫƱƳǓᲦዓƘ exp ‫܇׆‬ƕԗඬૠ γg · v ưਰѣƢǔᲨƭǇǓᲦਰѣᩓ‫ ئ‬F (t )vƸᲦᡞ఍‫܇‬șǯȈȫ g ƴǑƬƯਰࠢșǯȈȫƱ
C

[001]

ԗඬૠƕൿǇǔ࠯᩿ඬƷ᣻ƶӳǘƤƱƳǔᲨܱᆰ᧓ưᎋƑǕƹᲦg Ƹኽ୒᩿Ʊɟ‫ݣ‬ɟ‫ࣖݣ‬ƠƯφ_BƓǓᲦ1/|g| ƕҾ‫܇‬᩿᧓ᨠƴ‫ࣖݣ‬ƢǔƷưᲦӲԗ

θ

A

Ion

[110]

ඬૠ঺ЎƸᲦƦǕƧǕ‫ࣖݣ‬ƢǔҾ‫܇‬᩿ǛǤǪȳƕᡫᢅƢǔԗඬૠƱਵƑǒǕǔᲨࢼƬƯ‫נ܍‬Ƣ

(b)

[110]

ǔኽ୒᩿ƷૠƩƚီƳǔԗඬૠ঺ЎƕྵǕᲦƜǕƸ᭗ഏƷਦૠǇưԃǊǔƱ໯ᨂƴƋǔƕᲦӷ଺ƴȕȸȪǨ̞ૠƸ‫ݱ‬ƞƘƳǔƨǊᲦྵܱႎƴМဇưƖǔҾ‫܇‬᩿ƷૠƸஊᨂưƋǔᲨƜƜưƸҾ‫܇‬ƕ໯ᨂƴɳǜưƍǔƱƍƏᢅᆉƷǋƱȕȸȪǨኢૠǛ̅ƬƨᜭᛯǛƠƨƕᲦྵ

_

[001]

[110]

ܱƴƸҾ‫܇‬ƷૠƸஊᨂưƋǓᲦƜǕƸȕȸȪǨǹȚǯȈȫƷࠢƱƳƬƯྵǕǔᲨ‫ ׋‬2(a) ƷǑƏ‫ ׋‬3: (a) ȀǤȤȢȳȉ‫׹‬ኽ୒ƷؕࡁșǯȈȫᲨ(b)(k, l, m) = (1, −1, −2) ưਦ‫ܭ‬ƞǕǔҾ‫܇‬᩿ǛᡫᢅƢǔǤǪȳ.

ƴ᭗ᡮǤǪȳƕ N ௏ƷҾ‫܇‬᩿Ǜᡮࡇ v ưᡫᢅƢǔƱƖƴज़ơǔႻʝ˺ဇƷȕȸȪǨǹȚǯȈ
ȫƸᲦɟƭƷҾ‫܇‬᩿ƱƷႻʝ˺ဇǹȚǯȈȫǛ

ƴǑǔȉȬǹȈǢȈȠƷᚇยƳƲǛᡫƠƯǑƏS0 (ω) ƱƠƯᲦǍƘ᬴ܱႎƴऴ‫إ‬ƕࢽǒǕǔǑƏƴƳƬƯƖƨ

|S(ω)|2 = |S0 (ω)|22ƱƜǖưƋǔᲨsin (N ωd/2v),(10)sin2 (ωd/2v)

ƱᘙƞǕǔ [1]ᲨƨƩƠ d ƸǤǪȳƷᡶᘍ૾Ӽƴ

3. ᬴ܱ૾ඥ

ƦƬƨҾ‫܇‬᩿ᣐЗƷԗ஖ưƋǔᲨҾ‫܇‬᩿Ʒ௏ૠ
N = 1, 3, 10, 100 Ʒ‫ئ‬ӳƴƭƍƯƷ |S(ω)|2 ǛᲦN 2

ࡸ (6) ưƸᲦǤǪȳƷज़ơǔਰѣᩓ‫ئ‬ƷԗඬૠưǹǱȸȫƠƯ‫ ׋‬2(b) ƴᅆƠƨᲨƭǇǓ N ƕ

ƕ γg · v ưƋǔƜƱǛᅆƠƨᲨƜƜưᲦ‫ ׋‬3(a)‫ٻ‬ƖƘƳǔƴƭǕƯǹȚǯȈȫƷࢍࡇƸ N 2 ƴƴᅆƢǑƏƴᲦǷȪǳȳኽ୒ᲢȀǤǢȢȳȉನൔ̊ƠƯ‫ف‬ьƠƯƓǓᲦӷ଺ƴƦƷࠢƸ 1/N ƴᡯᲣǛ‫ܭ‬፯ƢǔƨǊƷؕࡁșǯȈȫǛ
⎧⎪A = (−1, 1, 0)a/2,⎪⎪⎨

ൔ̊ƠƯέᥘƴƳƬƯƍƘᲨҾྸႎƴƸ೅ႎƷኽ୒ǛҽƘƠƯႻʝ˺ဇƢǔҾ‫܇‬ƷૠǛ‫ف‬ǍƢ

⎪
⎪
⎪
⎩

ƜƱư Q ͌Ʒ᭗ƍσᯚƕ஖ࢳưƖǔǘƚƩƕᲦྵܱႎƳɥᨂƸǤǪȳᐯ៲ƕ೅ႎҾ‫܇‬ƱǳȒȸ

B = (0, 0, 1)a,(11)

C = (1, 1, 0)a/2,

ȬȳȈƴႻʝ˺ဇƢǔƜƱƷưƖǔ࠯‫ר‬ᐯဌᘍƷǑƏƴƱǔƱᲦȟȩȸਦૠ (k, l, m) ǛဇƍƯᆉưൿǇǔᲨƜƷុᩉƸɼƴᘔᆳƷૺ᩿ᆢưൿᡞ఍‫܇‬șǯȈȫƸ
gk,l,m = kA∗ + lB∗ + mC∗ ,ǇǔƷưλ‫ݧ‬ǤǪȳƷఋᆔǍǨȍȫǮȸᲦ೅ႎ(12)ƴǑƬƯ‫٭‬ǘǔƕᲦ঻ŷƷ᬴ܱவˑƴƓƍƯƸ

ƱᘙƞǕǔᲨƨƩƠ A∗ ᲦB∗ ᲦC∗ ƸƦǕƧǕᡞૠ μm ƷǪȸȀȸưƋǔƱᙸᆢǋǒǕƯƓǓᲦ఍‫܇‬ᆰ᧓ƷؕࡁșǯȈȫưƋǔᲨ ‫ ׋‬3(b) ƸᲦႻ࢘ƢǔҾ‫܇‬ૠƱƠƯƸૠ 1000 ̾ưƋǔᲨƜǤǪȳƕ g1,−1,−2 ưᘙƞǕǔҾ‫܇‬᩿ǛᡫᢅƠƯƷǑƏƳ‫˳׍‬ɶƷǳȒȸȬȳǹᧈƞƴ᧙Ƣǔᜭƍǔಮ‫܇‬ǛᅆƠƯƍǔᲨ(12) ࡸư‫ܭ‬፯Ơƨᡞ఍ᛯƸᲦஇᡈƷᕓᐏǛ̅ဇƠƨ᬴ܱǍᲦᲬ᣻σᯚ‫܇‬șǯȈȫ gk,l,m ǛဇƍǔƱᲨ‫ࣖݣ‬Ƣǔԗඬૠ

7

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㻿㼕㻔㻸㼕㻕᳨ฟჾ䠄㖄┤᪉ྥ䠅
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᳨ฟჾ

䠎ḟඖ
఩⨨᳨ฟჾ

㟁Ꮚศᯒ⏝
㟁☢▼

౯ᩘ㑅ู⏝
㟁☢▼

θ

㼤

㻿㼕㻔㻸㼕㻕᳨ฟჾ䠄㖄┤᪉ྥ䠅

㻞㼜㼥

㼤

㻞㼜㼦

㻞㼜㼤

㻿㼕㻔㻸㼕㻕᳨ฟჾ䠄Ỉᖹ᪉ྥ䠅㼦㼥φ㻿㼕㻔㻸㼕㻕᳨ฟჾ䠄Ỉᖹ᪉ྥ䠅㼦㼥ᶆⓗ⤖ᬗ‫ ׋‬4: (a) ᬴ܱᘺፗಒဦ‫׋‬Შ೅ႎኽ୒ƸǴȋǪȡȸǿȸƴȞǦȳȈƞǕƯƍǔᲨ(b) ѕឪཞ७ƷӲᄬൢǵȖȬșȫᲢ2px ᲦᲨ
2py Ღ2pz ᲣƔǒᐯ໱્ЈƞǕǔ X ዴƷᚌࡇЎࠋᲦӏƼ౨Ј֥ƷᣐፗᲢǤǪȳ᩺ഥኒᲣνk,l,m ƸᲦλ‫ݧ‬ᚌ θ, φ Ʒ᧙ૠƱƠƯᲦνk,l,m (θ, φ)

RCE வˑƕ฼ƨƞǕƨ଺ƴᩓᩉлӳƕ‫ف‬ь= γv · g√γv √={( 2k cos φ + 2m sin φ) cos θ + l sin θ},aƢǔƨǊᲦᒵᩓᢠКᩓᄬჽƱᲬഏΨˮፗ౨Ј֥ƴǑƬƯᡢᢅǤǪȳƷ̖ૠЎࠋǛย‫ܭ‬
ƢǔᲨ

(13)
ƱࢽǒǕǔᲨƜǕƕǤǪȳƷᢟᆆǨȍȫǮȸ ΔE

3. ્Јᩓ‫܇‬ƷᚇยƱɟᐲƢǔ଺ᲦƢƳǘƪ ΔE = hνk,l,m (θ, φ) Ǜ฼̖ૠЎࠋƷย‫ܭ‬ƱӷơᚇยҾྸưƋǔƕᲦƨƢƱƖƴ RCE ƕឪƜǓࢽǔᲨǤǪȳƷ̖ૠưƸƳƘᲦᘔᆳᩓᩉƴǑƬƯ᬴ܱႎƴƸᲦ೅ႎኽ୒Ǜ᭗ችࡇ‫᠃ׅ‬ᘺፗᲢǴȋǤǪȳƔǒеƕƞǕƨᩓ‫܇‬ƦƷǋƷǛᚇยǪȡȸǿȸᲣƴȞǦȳȈƠᲦǤǪȳȓȸȠƴ‫ݣ‬ƠƢǔᲨǤǪȳƔǒеƕƞǕƨᩓ‫܇‬ƸǤǪȳƯችࡇǑƘኽ୒ƷᚌࡇǛᛦራƢǔƜƱưᲦǤǪȓȸȠƱሁᡮࡇư᫠ǜưƍǔƨǊᲢǳȳȜȳƕज़ơǔԗඬૠǛǹǭȣȳƢǔƜƱƕưƖǔ

Ǥᩓ‫܇‬Უ
Ღኽ୒Ʒࢸ૾ƴ‫׹ݱ‬ƷᩓᄬჽǛፗƍᲢ‫ ׋‬4(a)ᲣᲨԗඬૠƕσᯚவˑǛ฼ƨƠƯ RCEƯᩓ‫܇‬ƷǈǛ 90 ࡇ͞ӼƠƯҞ‫˳ݰ‬౨Ј֥ưƕឪƜǕƹѕឪƞǕƨǤǪȳȓȸȠƔǒƷᏮѕ౨ЈƢǔᲨឪήƕᚇยƞǕᲦǇƨኽ୒ϋưƷᩓ‫ڂ੷܇‬ᄩྙƜǕǒᲭƭƷ৖ඥƸƦǕƧǕီƳƬƨМໜǛƴǋ‫҄٭‬ƕྵǕǔƨǊᲦˌɦᲭƭƷ৖ඥǛဇƍǋƪᲦX ዴƷᚇยƴƓƍƯƸƦƷ્ЈᚌࡇЎࠋƯƜǕǒƷ‫҄٭‬ǛᚇยƢǔᲨƔǒѕឪཞ७ƷᄬൢǵȖȬșȫƴ᧙Ƣǔऴ‫إ‬Ǜ

1. ᏮѕឪήƷᚇยࢽǔƜƱƕưƖǔᲨɟ૾ư̖ૠЎࠋƷᚇยưƸƍǇ‫ݣ‬ᝋƱƠƯƍǔ RCE ᢟᆆƸ X ዴ᪸؏ᡢᢅǤǪȳμƯǛᲬഏΨˮፗ౨Ј֥ư౨ЈƢǔưƋǔƷưᲦѕឪǤǪȳƸ X ዴǛᐯ໱્ЈƨǊ౨ЈјྙƸ 100%ưƋǓᲦǇƨᩓ‫܇‬ƷᚇยƠƯؕࡁཞ७ǁᏮѕឪƢǔᲨƜƷ X ዴӓ᣽ưƸᘔᆳᩓᩉƱᐯѣᩓᩉƴǑƬƯ્ЈƞǕƨᩓǛᲦλ‫ݧ‬ᚌࡇƷ᧙ૠƱƠƯ Si(Li)X ዴ౨Ј‫܇‬ǛƦƷǨȍȫǮȸƔǒғКƠƯᚇยưƖǔǄ֥ưᚘยƢǔᲨƔᲦƦƷᢃѣ᣽ࠢƴƸளጉཞ७ƷǳȳȗȈȳȗ

2. ̖ૠЎࠋƷᚇยȭȕǡǤȫƕӒପƞǕǔᲨƜǕǒƷ৖ඥǛᢘ‫ܯ‬ኽ୒ϋưσᯚႎƴѕឪƞǕƨǤǪȳƸᲦኽኵǈӳǘƤǔƜƱưҾ‫܇‬ཞ७ǍσᯚȀǤȊȟǯ

୒Ҿ‫܇‬ƱƷᘔᆳƴǑƬƯᩓᩉлӳƕ‫ف‬ьƢǹƴ᧙̞ƢǔಮŷƳȇȸǿǛӕࢽƢǔƜƱƕư

ǔᲨ̊Ƒƹ൦እಮǤǪȳƷ 1s ᩓ‫܇‬Ʊ 2p ᩓƖǔƕᲦஜᆜưƸɼƴᏮѕឪ X ዴƷᚇยኽௐƴ‫܇‬ưƸᩓᩉૺ᩿ᆢƕኖᲮ̿ီƳǔᲨࢼƬƯ໰ໜǛ዁ƬƯᚐᛟƢǔᲨ

8㻌㻌㼇㼐㼑㼓㻚㼉
ධᑕゅᗘ 㻌 䃗㻔㼍㻕㻌㻭㼞㻝㻢㻗

4. ᄬൢǵȖȬșȫǛཎ‫ܭ‬ƠƨҾ‫܇‬ཞ७Сࣂ

㻝㻚㻜

㻡㻚㻠

㻔㻝㻘㻙㻝㻘㻜㻕

ǤǪȳ᩺ഥኒƴƓƚǔਰѣኽ୒‫ ئ‬F (t ) ƸᲦࡸ

㻡㻚㻟

㻡㻚㻞

㼤

㻢㻚㻜

㻡㻚㻥

㻔㻝㻘㻙㻝㻘㻙㻞㻕㻡㻚㻤㼄⥺ᙉᗘ㻌㼇㼍㼞㼎㻚㼉঺ЎƷ᣻ƶӳǘƤưƋǔᲨƜƷƏƪƷƻƱƭƕ
ǤǪȳƷᢟᆆǨȍȫǮȸƴɟᐲƠƯσᯚѕឪƕឪƜǔƨǊᲦRCE ƸႺዴ͞ήƠƨ X ዴȬȸǶȸ

㻢㻚㻠

㻢㻚㻟

㼤

㻙㼥

㻙㼥

㼦

㼦
Ỉᖹ᪉ྥ
㖄┤᪉ྥ

㻟㻝㻟㻡 㻟㻝㻠㻜 㻟㻝㻠㻡㻟㻝㻟㻡 㻟㻝㻠㻜 㻟㻝㻠㻡

㼦

㻜㻚㻢

㻢㻚㻡

㻔㻝㻘㻙㻝㻘㻙㻠㻕㻜㻚㻤Ტ6ᲣǑǓᲦӲŷƷ͞ή૾ӼƱԗඬૠǛǋƭਰѣ

㻢㻚㻢

㼤

㻜㻚㻠
㻜㻚㻞
㻜㻚㻜

ƴǑǔήѕឪƴႻ࢘ƢǔᲨᚕƍ੭ƑǕƹᲦσᯚ㻟㻝㻟㻡 㻟㻝㻠㻜 㻟㻝㻠㻡ບ㉳䜶䝛䝹䜼䞊㻌㼇㼑㼂㼉ƴМဇƢǔᡞ఍‫܇‬șǯȈȫ gklm Ǜᢠ৸ƢǔƜ

ධᑕゅᗘ 㻌 䃗㻌㻌㼇㼐㼑㼓㻚㼉

㻔㼎㻕㻌㻲㼑㻞㻠㻗㻝㻚㻜ȫǛཎ‫ܭ‬ƠƨҾ‫܇‬ཞ७ƷǳȳȈȭȸȫƕӧᏡƱ

㻜㻚㻤

㻙㼥

㻙㼥

㻙㼥

㻜㻚㻢

㼦

㼦

㼦
Ỉᖹ᪉ྥ
㖄┤᪉ྥ

㻢㻢㻥㻡 㻢㻣㻜㻜 㻢㻣㻜㻡㻢㻢㻥㻡 㻢㻣㻜㻜 㻢㻣㻜㻡㼄⥺ᙉᗘ㻌㼇㼍㼞㼎㻚㼉ƱưᲦਰѣᩓ‫ئ‬Ʒ͞ήǛСࣂƠᲦᄬൢǵȖȬșƳǔᲨ‫ ׋‬5(a) Ʊ (b) ƸᲦಮŷƳ gklm ƴ‫ࣖݣ‬Ƣǔԗඬૠ঺ЎǛМဇƠƯ 416 MeV/u Ʒ He-like

Ar16+ ᲦƓǑƼ 423 MeV/u Ʒ He-like Fe24+ ǤǪȳƷ RCEᲢ1s2 1 S0 → 1s2p 1 P1 ᲣǛᚇยƠƨኽௐǛᘙƠƯƍǔᲨƦǕƧǕ φ = −0.23◦ Ღ−0.11◦

㻞㻚㻥

㻞㻚㻤

㻞㻚㻣

㻟㻚㻞

㻔㻞㻘㻙㻝㻘㻙㻝㻕 㼤

㻟㻚㻝

㻟㻚㻜

㻟㻚㻡

㻔㻞㻘㻙㻝㻘㻙㻟㻕 㼤

㻟㻚㻠

㻟㻚㻟

㻟㻚㻞

㻔㻞㻘㻙㻝㻘㻙㻡㻕 㼤

㻜㻚㻠
㻜㻚㻞
㻜㻚㻜

㻢㻢㻥㻡 㻢㻣㻜㻜 㻢㻣㻜㻡ບ㉳䜶䝛䝹䜼䞊㻌㼇㼑㼂㼉ƴƓƍƯ θ Ǜឥ௹ƠƨᲨ ್᠆Ƹλ‫ݧ‬ᚌࡇ θᲦӏ㻔㼏㻕㻌Ƽࡸ (13) ǛဇƍƯ‫٭‬੭ƞǕƨѕឪǨȍȫǮȸᲦጏ᠆Ƹ Si(Li) ౨Ј֥Ტ൦࠯ᲦᤲႺᲣƴƓƚǔᏮѕឪ X ዴӓ᣽ưƋǓᲦRCE வˑƕ฼ƨƞǕƨλ‫ݧ‬ᚌƴᥘƍȔȸǯǛਤƭƱƱǋƴᲦƦǕƧǕ᫋ᓸƳ્ЈᚌЎࠋǛᅆƠƯƍǔᲨ(1,-1,0) ঺ЎưѕឪƞǕƨ‫ئ‬ӳƸ൦࠯૾ӼƴൔǂƯᤲႺ૾ӼƷ‫ ׋‬5: (a)416 MeV/u Ar16+ ǤǪȳᲦƓǑƼ (b) 423
MeV/u Fe24+ ǤǪȳǛᲦಮŷƳԗඬૠ঺ЎǛဇƍƯ 1s2p ƴѕឪƠƨᨥƴࢽǒǕƨᲦ൦࠯ᲦᤲႺ
૾ӼƷᏮѕឪ X ዴࢍࡇᲨ̅ဇƠƨԗඬૠ঺Ўƴ‫ࣖݣ‬Ƣǔȟȩȸਦૠ (k, l, m) ƱҾ‫܇‬᩿ƷӼƖǛ௒ϋƴᅆƠƯƋǔᲨ(c)IᤲႺ /I൦࠯ Ʒ᬴ܱ͌Ʊᚘም͌[11]Შ

ࢍࡇƕ̿ˌɥưƋǔƷƴ‫ݣ‬ƠᲦ(1,-1,-2) ঺ЎưƸƦƷࢍࡇൔƕᡞ᠃ƠƯƍǔᲨƞǒƴ (1,-1,-4)঺ЎưƸ൦࠯૾ӼƴƸǄƱǜƲ X ዴƕ౨ЈƞǕƯƍƳƍᲨFe24+ ǤǪȳƷ‫ئ‬ӳǋͼӼƸӷಮưᲦȟȩȸਦૠ m ƕ‫ٻ‬ƖƘƳƬƯҾ‫܇‬᩿ƕ͂ǕƯƍƘƴࢼƬƯਰѣᩓ‫ئ‬Ʒ͞ή૾ӼƸ x ૾ӼƴͼƖᲦǔ X ዴࢍࡇƷൔ IᤲႺ /I൦࠯ ǛᙸᆢǋǔƱ‫ ׋‬5(c)൦࠯૾ӼǁƷ્ЈƕΟѬƴƳƬƯƍƘᲨƷǑƏƴƳǓᲦ᬴ܱ͌Ʊ᩼ࠝƴᑣƘɟᐲƠƯƍƍǇ 2p Ɣǒ 1s ཞ७ǁƷᏮѕឪƸᩓൢӑಊ‫܇‬ᢟǔᲨƜǕƸႺዴ͞ήƠƨਰѣኽ୒‫ئ‬ǛဇƍƯѕᆆưƋǔƷưᲦX ዴƷ્ЈᚌࡇЎࠋ I(ξ) Ƹӑಊឪཞ७ƷǢȩǤȡȳȈƕܱྵƞǕƯƓǓᲦƞǒ

2‫܇‬ȢȸȡȳȈƔǒƷᚌࡇ ξ ƴ‫ݣ‬ƠƯ I(ξ) = sin ξƴ gklm Ǜᢠ৸ƢǔƜƱưƦƷ૾ӼƕСࣂưƖƯƷЎࠋǛਤƭᲨǤǪȳ᩺ഥኒƴƓƍƯ 2px Ღ2py ᲦƍǔƜƱǛᅆƠƯƍǔᲨ2pz ӲᄬൢиแˮƔǒƷᏮѕឪήƷᚌࡇЎࠋǛƜƷǑƏƳ৖ඥǛဇƍǔƱᲦ‫˳׍‬ϋƷᘔᆳǍᘙƢƱ‫ ׋‬4(b) ƷǑƏƴƳǓᲦᤲႺ૾ӼƷ౨Ј֥ǨȍȫǮȸ੷‫ڂ‬ሁƴƓƚǔҾ‫܇‬Ʒϋᢿཞ७ǍඬƸ 2py Ʊ 2pz Ღ൦࠯૾ӼƷ౨Ј֥Ƹ 2px Ʊ 2pz ཞѣ᧙ૠƷ࢟ᲦӼƖƷјௐƳƲƴ᧙ᡲƠƨᛇኬƳ७ƔǒƷႆήǛ౨ЈӧᏡưƋǔᲨਰѣᩓ‫ئ‬Ʒ͞ȀǤȊȟǯǹƷᚐଢǁӼƚƨૼƨƳ᬴ܱႎᄂᆮ

ή૾ӼƸ (7) ࡸưɨƑǒǕǔƨǊᲦӲиแˮǁƷǁƷ‫᧏ޒ‬ƕ஖ࢳƞǕǔᲨǇƨኽ୒ɶưᡶᘍ૾ӼѕឪᄩྙǛᎋॾƠƯᤲႺȷ൦࠯૾Ӽǁ્ЈƞǕƴǢȩǤȳƞǕƨཞ७Ɣǒ્ЈƞǕǔᩓ‫܇‬ƷᲦ

9

0.5

0

㞫ㄢ hδc

P1

2

P1/2

2

P3/2

0.5

1s2p (1P1)

15.03 eV113139.55 eV(a)䜯䝇䝛䝮䝷䜴

䝛䝱䞀䝚

1s2s (1S0)
9.3 x 10-15 s
2.3 x 10-9 s

1
1

0.5

0

0.5

Tilt angle θ [deg.](b) Ar17+
1.6

X-ray yields [arb.]

3.0
2.5

1

1.7

1.8

x

1.8

1.9

2

2.1

x

2.0

z

1.5

1s2 (1S0)

2.1

2.2

2.3

2.4

‫ ׋‬7:x-y-yǛСࣂƠƯᚌࡇီ૾ࣱǛјྙǑƘᚇยƢǔƜƱ

z

z
Ỉᖹ᪉ྥ
㖄┤᪉ྥ

ƕӧᏡưƋǔᲨƜǕƸ Si(Li) ౨Ј֥ǛМဇƢǔ

1.0ƜƱưኽ୒Ўή֥ሁƴൔǂƯ‫ࠢٻ‬ƴ‫ٻ‬Ɩƍ౨Јᇌ˳ᚌǛࢽƳƕǒǋᲦǨȍȫǮȸЎᚐᏡᐯ៲Ƹ

0.5
0.0

j = 1/2

j = 3/2

3315 3320

j = 1/2

3325

j = 1/2

j = 3/2

3315 3320

3325

j = 3/2

3315 3320

౨Ј֥ưƸƳƘ೅ႎኽ୒ƷᚌࡇЎᚐᏡưൿǇǔ

3325

Transition energy [eV]‫ ׋‬6:

ȘȪǦȠಮ Ar16+ Ʒ Λ ‫׹‬ᲭแˮኒᲨ

ƔǒưƋǓᲦȬȸǶȸᛔឪᖩήᲢLIFᲣЎήƳƲ(a) 1s2p (1 P)ᲦƓǑƼ 2p (2 P) ƔǒƷᏮѕឪήƱӷಮƷย‫ܭ‬ҾྸưƋǔᲨƷӑಊ‫܇‬ȢȸȡȳȈƴ‫ݣ‬Ƣǔ્ЈᚌࡇЎࠋᲨ(b)390 MeV/u Ʒ൦እಮ Ar17+ ǤǪȳǛᲦಮŷƳԗඬૠ঺ЎǛဇƍƯ 2p ǁѕឪƠƨᨥƴࢽǒǕƨᲦ൦࠯ᲦᤲႺ૾ӼƷᏮѕឪ X ዴࢍࡇᲨᲬƭƷȔȸǯƕƦǕƧǕ 2p1/2 Ღ2p3/2 ǁƷ RCE ƴ‫ࣖݣ‬ƢǔᲨ

5. X ዴ-VUV ᪸؏ƷᲬ᣻σᯚਰѣኽ୒‫ئ‬ƷᲬƭƷԗඬૠ঺ЎǛӷ଺ƴМဇǢȳȁǫǹȗ‫׹‬ǳȳȗȈȳȗȭȕǡǤȫ [13] ƷƢǔƱᲦᲭแˮኒƴƓƚǔᲬ᣻σᯚ᬴ܱǛᘍƏƜᚇยƴӼƚƨ᬴ܱǋᡶᘍɶưƋǔᲨƱƕưƖǔᲨီƳǔᲬแˮ᧓ƷᢟᆆǨȍȫǮȸλ‫ݧ‬ǤǪȳƕ൦እಮƷ‫ئ‬ӳƸǹȔȳ៽ᢊႻʝ˺ဇƴǑƬƯ៽ᢊᚌᢃѣ᣽Ʒᄬൢ᣽‫܇‬ૠƸᲦǑƍ᣽‫܇‬ૠưƸƳƘƳǔᲨƦƷኽௐᲦƜǕǒƷཞ७ƔǒƷᏮѕឪήƷ્‫ݧ‬ᚌࡇЎࠋƸᲦI(ξ) =⎧⎨1(for 2p1/2 ),⎩ (1 − 3 cos 2ξ)/2(for 2p3/2 ),5

ΔE1 ᲦΔE2 ƴ‫ݣ‬ƠƯ
⎧⎨ ΔE1 =

hνk,l,m (θ, φ),⎩ ΔE =
2hνk ,l ,m (θ, φ),(15)ƷƱƖᲬ᣻σᯚவˑƕ฼ƨƞǕᲦඬᧈƷီƳǔ

(14)

ᲬƭƷσᯚήǛӷ଺ƴༀ‫ݧ‬ƢǔƜƱƴႻ࢘Ƣǔ[15]Შ̊Ƒƹ‫ ׋‬7 ƷǑƏƳ Λ ‫׹‬ƷᲭแˮኒƴƓƍƱƳǔ [14]ᲨƭǇǓ‫ ׋‬6(a) ƴᅆƢǑƏƴᲦ2p1/2

ƯᲦν0,0,−2 ƕ 21 P - 21 S ᢟᆆ (15.03 eV)Ღν1,−1,−2ƔǒƷ્‫ݧ‬Ƹ‫ܦ‬μƴሁ૾ႎƱƳǓᲦ2p3/2 Ƹӑಊƕ 11 S - 21 P ᢟᆆᲢ3139.55 eVᲣƷσᯚவˑǛƦ‫ݧ્܇‬ƕǍǍɺǈǛƓƼƨǑƏƳ࢟ƴƳǔᲨƜǕƧǕ฼ƨƢǑƏƳவˑư᬴ܱǛᘍƏƜƱƕӧǕǛ 390 MeV/u Ʒ H-like Ar17+ ǤǪȳǛဇƍᏡưƋǔᲨƞǒƴᲦࡸ (13) ǑǓᲦθ  1 ƷவˑƯܱᨥƴย‫ܭ‬ƢǔƱ‫ ׋‬6(b) ƷǑƏƴƳǓᲦ2p1/2

ɦưƸ ν0,0,−2 Ƹ θ ƴ̔‫܍‬ƠƳƍƨǊᲦθ ‫᠃ׅ‬ƴƔǒƷ્‫ݧ‬ƴƸီ૾ࣱƕᚇยƞǕƳƔƬƨᲨɟǑƬƯ ν1,−1,−2 ƷǈǛҥ཯ƴǹǭȣȳƢǔƜƱ

૾ 2p3/2 ƔǒƷ્‫ݧ‬ƴƸီ૾ࣱƕസǔǋƷƷᲦӷƕưƖᲦƜǕƸǇƞƴ X ዴ᪸؏ƴƓƍƯ RCEவˑưย‫ܭ‬Ơƨ He-like ǤǪȳᲢ‫ ׋‬5(a)ᲣƱൔǛМဇƠƨȝȳȗȷȗȭȸȖ᬴ܱƕӧᏡƳƜƱ᠋ƢǔƱƦƷီ૾ࣱƸࢊǇǔͼӼƱƳǓᲦྸᛯǛॖԛƢǔᲨƜƜưƸ ν0,0,−2 Ღν1,−1,−2 ǛƦǕƧƱɟᐲƢǔᲨƜƷǑƏƴᲦᲭഏΨǳȒȸȬȳȈǕǫȃȗȪȳǰԗඬૠᲦȗȭȸȖԗඬૠƱԠƿᲨσᯚѕឪǛဇƍǔƱ 2p ཞ७ƷࣇኬನᡯǛЎᩉƢǫȃȗȪȳǰԗඬૠǛ‫ܭ׍‬Ơƨཞ७ưȗȭȸȖǔǄƲƷǨȍȫǮȸЎᚐᏡǛਤƪƳƕǒᲦ͞ήԗඬૠǛǹǭȣȳƠƨᨥƴࢽǒǕƨ X ዴƷӓ᣽10Ǜ‫ ׋‬8(a) ƴᅆƠƨᲨ ƨƩƠᲦ1̔‫܍‬ƠƯǷȕȈƠᲦδc = 0 ưƸ‫ܦ‬μƴᲬƭƴЎ1hδc = ΔE[2 P-2 S] − hν0,0,−2 , (16)ᘷƠƯƍǔᲨƜǕƸ Autler-TownesᲢATᲣᲬ᣻ƸǫȃȗȪȳǰƷᩉᛦưƋǔᲢ‫ ׋‬7ᲣᲨᤲႺ૾Ӽ᪮ƱԠƹǕᲦᩓᄬ‫ئ‬ƱƷࢍƍႻʝ˺ဇƴǑƬƯưࢽǒǕƨǹȚǯȈȫƸ 11 S-21 P ƷᢟᆆǨȍȫҾ‫܇‬ƷǨȍȫǮȸแˮƕȩȓЎᘷƢǔƜƱƴឪǮȸᲢ3139.55 eVᲣƴ RCE ƷσᯚȔȸǯǛǋƭ‫׆‬Ƣǔ [16]ᲨAT Წ᣻᪮Ƹ᭗ࢍࡇȬȸǶȸЎήƷƴ‫ݣ‬ƠƯᲦ൦࠯૾ӼưƸȔȸǯƷˮፗƕ δc ƴƳƲưƠƹƠƹྵǕᲦȉȬǹȈǢȈȠᲢήƷᘘǛǇƱƬƨҾ‫܇‬ᲣƱƍƏಒࣞƴǑƬƯႺज़ႎƴᛟଢƞǕǔ [17, 18]Შ᬴ܱưࢽǒǕƨ AT Წ᣻᪮ƷȔȸǯˮፗǛᩉᛦ hδc Ʒ᧙ૠƱƠƯȗȭȃȈƢ

㻔㼍㻕ǔƱᲢ‫׋‬Ჲ (b)ᲣᲦ“avoided level crossing”Ʒಮ‫܇‬Horizontal
VerticalƕࢽǒǕǔᲨܱዴƓǑƼໜዴƸᲦΩ0 = 0, 3.4 eVƴƭƍƯᲦɟᑍႎƳȉȬǹȈǢȈȠ೉‫׹‬ƴǑƬhδc = 2.4 eVƯᚘምƠƨȉȬǹȈཞ७ǁƷᢟᆆǨȍȫǮȸ

ΔE ± = ΔE[11 S-21 P] ± hδ = 1.2 eV

(17)

c

Normalized X-ray Yield [eV]

Ω20 + δc2 ,ưƋǔᲨƨƩƠ Ω0 Ƹ 21 P - 21 S ᧓ƷȩȓԗඬૠưƋǓᲦδc = 0 ƷǹȚǯȈȫƷЎᘷࠢƔǒࢽǒǕƨ᬴ܱ͌Ტ3.4 eVᲣǛ̅ဇƠƨᲨ᬴ܱኽௐ

hδc = 0 eVƸᙸʙƴᚘም͌ƴࢼƬƯƓǓᲦȬȸǶȸༀ‫ݧ‬Ʊӷಮƴ᭗ࢍࡇƷਰѣኽ୒‫ئ‬ƴǑƬƯǋȉȬǹȈ
ཞ७ƕ࢟঺ƞǕǔƜƱǛᚇยƠƨ [10]ᲨƜǕƸhδ = -1.1 eVcኽ୒‫ئ‬ƴǑƬƯ 2s − 2p ᧓ƕࢍƘኽӳƞǕᲦᲬཞ७Ʒዴ࢟ኽӳưᘙƞǕǔǑƏƳǳȒȸȬȳȈƳ᣽‫܇‬ཞ७ƕưƖƯƍǔƜƱǛᅆƠƯƍǔᲨƜƷǑƏƳ AT Წ᣻᪮ƕᚇยƞǕǔƨǊƴƸ‫ݲ‬ƳƘhδc = -2.3 eVƱǋȩȓਰѣƷԗ஖ƷᲬ̿ᆉࡇƷǳȒȸȬȳǹ
3130

3135

3140

3145

3150

଺᧓ƕ࣏ᙲưƋǓᲦƍǇȩȓԗඬૠƕ 3.4 eV ư

Probing Energy [eV]ƋǔƜƱƔǒᲦǤǪȳƸૠ μm ƷុᩉǛ 2s − 2p䝥䝻䞊䝤࿘Ἴᩘ㻌㼇㼑㼂㼉㻔㼎㻕 3150᧓ƷˮႻऴ‫إ‬Ǜ̬ƬƨǇǇᡶǜưƍǔƱƍƏƜᐇ㦂್ィ⟬್䠄㻌㻌㻌㻌㻌㻌㻌㻩㻌㻟㻚㻠㻌㼑㼂䠅ィ⟬್䠄㻌㻌㻌㻌㻌㻌㻌㻩㻌㻜㻌㼑㼂䠅

3145

ƱƴƳǔᲨ
ƞƯᲦ‫ ׋‬8(a) ƴƓƍƯᲦᤲႺ૾ӼƷǹȚǯȈȫ

3140

ưƸ AT Წ᣻᪮ƕᚇยƞǕƯƍƳƔƬƨƕᲦƜǕ
3135

ƸЭ᪮ưᚐᛟƠƨਰѣᩓ‫ئ‬Ʒ͞ήƴขƘ᧙̞Ơ

3130
-8

ƯƍǔᲨƍǇǫȃȗȪȳǰƴ̅ƬƯƍǔ ν0,0,−2
-6

-4

-2

0

2

4

6

8

ƸᲦࡸᲢ7ᲣǑǓ x ૾Ӽƴ͞ήƠƯƓǓᲦɟ૾ư䜹䝑䝥䝸䞁䜾࿘Ἴᩘ䛾㞳ㄪ㻌㻌㻌㻌㻌㻌㻌㻌㼇㼑㼂㼉‫ ׋‬4(b) ǑǓᤲႺ૾ӼƷ౨Ј֥Ƹ 2px ƔǒƷႆή‫ ׋‬8: (a) ǫȃȗȪȳǰԗඬૠƷᩉᛦ δ Ǜ‫ܭ׍‬ƠƯȗȭȸȖԗඬૠǛǹǭȣȳƠƨƱƖƷ 416 MeV/u
Ar16+ ƷᏮѕឪ X ዴӓ᣽Შ(b) ᩉᛦ δ ƴ‫ݣ‬ƢǔσᯚȔȸǯˮፗƷ‫҄٭‬ᲢX ዴưƸƳƘ̖ૠЎࠋƷย‫ܭ‬ኽௐǛ̅ဇᲣᲨܱዴƸȉȬǹȈǢȈȠ೉‫׹‬ƴǑǔᚘም͌ [10]ᲨǛ౨ЈưƖƳƍᲨƭǇǓ‫׋‬Ჳ (a) ƷǑƏƴᲦȉȬǹȈཞ७Ǜ࢟঺ƠƯƍǔƷƸƻƱƭƷ 2px иแˮƩƚưᲦ2py ƓǑƼ 2pz Ƹ໯અѣཞ७ᲢҾ‫܇‬ȏȟȫȈȋǢȳƷ‫׍‬ஊཞ७ᲣƷǇǇưƋǔƱ

11ʖेưƖǔᲨƜǕƸ͞ήСࣂƴǑƬƯᄬൢиแήѕឪƴƓƍƯҾ‫܇‬ƕᩓᄬ‫ئ‬Ʊή‫܇‬ƷǍǓӕǓˮǛཎ‫ܭ‬ƠƨȗȭȸȖǛᘍƏƜƱư᬴ܱႎƴᄩǛƢǔƷƴ‫ݣ‬ƠƯᲦRCE ưƸǤǪȳƸኽ୒‫ئ‬ƔƔǊǒǕǔᲨ‫ ׋‬9(b) ƸȗȭȸȖƴМဇƢǔ͞ήǒႺ੗ǨȍȫǮȸǛӖƚӕǔƜƱƸƳƍᲨܱƸƷӼƖǛ‫҄٭‬ƞƤƨኽௐưƋǓᲦǫȃȗȪȳǰ

RCE ƷѕឪǨȍȫǮȸเƸǤǪȳƷɳᡶᢃѣƱ‫׶‬Ⴚ૾Ӽƴ͞ήƠƨȗȭȸȖԗඬૠ ν1,−1,0 ǛưƋǓᲦƜǕƕήѕឪƱఌஜႎƴီƳǔໜưƋМဇƢǔƱ AT Წ᣻᪮ƸμƘᚇยƞǕƳƍᲨƜǔᲨƜƷໜǛჳႽ໯ƘӕǓλǕᲦȉȬǹȈǢȈ

ǕƸ ν1,−1,0 ƕ 2px иแˮǛѕឪƠƳƍƔǒưƋ

Ƞ೉‫׹‬Ǜ̲ദƠƨ࢟ư RCE ǛᛟଢƢǔƜƱƕ

ǓᲦɟ૾ư͞ή૾ӼƕǫȃȗȪȳǰƱǄǅ࠯ᘍưƖǔᲨưƋǔ ν1,−1,4 ǛМဇƢǔƱᲦAT Წ᣻᪮Ǜ࢟঺ǇƣቇҥƷƨǊƴ‫ ׋‬10(a) ƷǑƏƳᲦǨȍȫƠƯƍǔ 2px ঺ЎƷǈǛᢠ৸ႎƴȗȭȸȖƢǔǮȸࠀƕ ω12 ưƋǔᲬแˮ |1Ღ|2 ǛਤƭҾ‫܇‬ƜƱƕЎƔǔᲨƜƷǑƏƴᲦ͞ήСࣂƱᲬ᣻σƱᲦF cos ωL t ưᘙƞǕǔȬȸǶȸ‫ئ‬ƷႻʝ˺ဇᯚƷȆǯȋȃǯǛኵǈӳǘƤǔƜƱưᄬൢǵȖǛᎋƑǔᲨஜ᪮ưƸ RCE Ʒ᣽‫܇‬ᛯႎƳ੨΂ǛȬșȫǛཎ‫ܭ‬ƠƨȝȳȗȷȗȭȸȖ᬴ܱƕᲦXǑǓႺज़ႎƴྸᚐƢǔƨǊƴ༁ᩃƳૠࡸǛᢤƚᲦዴƓǑƼ VUV ᪸؏ưܱྵƞǕǔ [11]Შ

᩼Ⴛ‫ݣ‬ᛯႎƳᜭᛯƴƱƲǊǔᲨɟᑍႎƳȉȬǹȈǢȈȠ೉‫׹‬ƴƓƍƯҾ‫܇‬Ʊᩓᄬ‫ئ‬ӏƼႻʝ˺ဇǛԃǊƨμኒƷȏȟȫȈȋǢȳ H ƸᲦH =6. ኽ୒‫ئ‬ƴǑǔ RCE Ʒ᣽‫܇‬ᛯ

HA + HL + VAL ƱᘙƞǕᲦஜᆜƷϔ᪽ưƸᲦਰѣኽ୒‫ئ‬ƴǑǔઅѣƷኽ

1
HA = ω12 (|22| − |11|),
2
HL = ωL (â† â),ௐƱƠƯҞӞχᛯႎƴ RCE ǛᛟଢƠƨƕᲦƜƜưƸ᣽‫܇‬ᛯႎƳӕৢƍƴƭƍƯᛯƣǔᲨƳƥ

(18)
(19)

VAL = −ed · F(|21| + |12|)(â† + â),ƳǒƹᲦЭ᪮ƷǑƏƳȉȬǹȈǢȈȠ೉‫׹‬Ǜਤ

(20)

ų

ƪЈƢƨǊƴƸᩓᄬ‫ئ‬Ʒᇹʚ᣽‫҄܇‬ƴǑǔƀήưƋǔᲨƨƩƠ â† ӏƼ â Ƹή‫܇‬Ʒဃ঺Ღෞ๒

‫܇‬ƁƷಒࣞƕ࣏ᙲƱƳǔƔǒưƋǔᲨƱƜǖƕ๫ም‫܇‬Ღd = 2|r|1 = 1|r|2 Ƹᩓ‫܇‬ӑಊ‫܇‬ᢟᆆƷᢟᆆᘍЗᙲእưƋǔ [19]Შ̊Ƒƹ‫ئ‬ƴή‫܇‬(a)ƕ N ̾ƋǓᲦҾ‫܇‬ƕɥแˮƴƍǔƱƖƷཞ७Ƹ|2|N  = |2, N  ƱᘙƞǕᲦ໯અѣཞ७Ʒ‫׍‬ஊ͌૾ᆉࡸƸ
ධᑕゅᗘ θ㻌㻌㼇㼐㼑㼓㻚㼉

(b)
1.0

5.4

㼄⥺ᙉᗘ㻌㼇㼍㼞㼎㻚㼉(1,-1,0)0.8

5.3

5.2 5.8䜹䝑䝥䝸䞁䜾

5.7(1,-1,-2)

5.6

5.5 6.1

䜹䝑䝥䝸䞁䜾

䝥䝻䞊䝤

䝥䝻䞊䝤

0.6

6

(1,-1,-4)

5.9(HA + HL )|2, N  =5.8䜹䝑䝥䝸䞁䜾

䝥䝻䞊䝤ƷǑƏƴƳǓᲦҾ‫܇‬ƷϋᢿǨȍȫǮȸƱή‫ئ܇‬ƷǨȍȫǮȸƷӳᚘƕኒƷ‫׍‬ஊǨȍȫǮȸƱƳǔᲨ

0.2
0.0


ω12
+ N ωL |2, N ,
2

(21)

Ỉᖹ᪉ྥ
㖄┤᪉ྥ

0.4



ƜǕǛ RCE ƴᢘဇƢǔƨǊᲦˌɦƷǑƏƴή
3135 3140 3145

3135 3140 3145

‫ئ܇‬ƷȏȟȫȈȋǢȳ HL ǛǤǪȳɳᡶᢃѣƷ

3135 3140 3145

ບ㉳䜶䝛䝹䜼䞊㻌㼇㼑㼂㼉ȏȟȫȈȋǢȳ HT ƴፗƖ੭ƑᲦႻʝ˺ဇȏȟȫ‫ ׋‬9: (a)2p ཞ७ƷǨȍȫǮȸแˮᲨǫȃȗȫƞǕƯƍ
Ƴƍཞ७Ტ߼ᲣƱᲦx ૾ӼƷႺዴ͞ήưǫȃȗȫƞ
Ǖƨཞ७ᲢӫᲣ
Შ(b)δ = 0 ƷவˑƴƓƍƯᲦಮŷƳԗඬૠ঺ЎưȗȭȸȖƠƨƱƖƷ X ዴࢍࡇᲨ̅
ဇƠƨ঺ЎᲦƓǑƼǫȃȗȪȳǰᲦȗȭȸȖƷႻ‫ݣ‬ႎƳ͞ή૾ӼǛ௒ϋƴᅆƠƯƋǔ [11]Შ

ȈȋǢȳ VAL ƴኽ୒ȝȆȳǷȣȫǛ̅ဇƢǔᲨ

12

(a)
EnergyEigenstate of
HA

Energy(b)(c)

Eigenstate of
HA+Hc

Eigenstate of
HAC= HA+HC+VAC‫ ׋‬10: (a) Ҿ‫܇‬Ʒϋᢿཞ७Ღ(b) Ҿ‫܇‬Ʒϋᢿཞ७+ɳᡶᢃѣᲦ(c) ኽ୒‫ئ‬ƴǑƬƯǫȃȗȫƞǕƨҾ‫܇‬Ʒϋᢿཞ७+ɳᡶᢃѣƷǨȍȫǮȸแˮᲨ

ƴႻʝ˺ဇƕƋǕƹ጑ᡚƕᚐƚƯǨȍȫǮȸƕ

2 ∇2
(22)
,
2M
VAL = −eVg exp{−2πig · (R + r)},HT = −

ЎᘷƠᲦૼƨƳ‫׍‬ஊཞ७Ǜ˺ǔᲨƜǕƕȉȬǹ
Ȉཞ७ưƋǔᲨ(23)Ⴛʝ˺ဇ VAL ǛԃǊƨμȏȟȫȈȋǢȳƸᲦƨƩƠ M ƸǤǪȳƷឋ᣽ưƋǔᲨƜǕǛဇƍǔ

|1, K + hgᲦ|2, K ǛșȸǹƱƠƨᘍЗᘙᅆƴƯᲦƱ໯અѣཞ७Ʒ‫׍‬ஊ͌૾ᆉࡸƸᲦǤǪȳƷɳᡶK2
hg · v hδ++, (26)
2M2
2
hg · v hδ
K2+−, (27)
H22 =
2M
2
2
Ω∗0
H12 =
(28)
,
2
Ω0
H21 =
(29)
,
2
ƱᘙƞǕᲦȩȓਰѣૠ Ω0 = |Ω0 |eiα ƸᲦᢃѣ᣽Ǜ K ƱƠƯᲦ
(HA + HT )|2, K =



ω12
K2
+
2
2M

H11 =


|2, K,(24)ƱƳǓᲦϋᢿǨȍȫǮȸƱɳᡶǨȍȫǮȸƷᚘƕ‫׍‬ஊ͌ƱƳǔᲨᡞ఍‫܇‬șǯȈȫ g ƕ RCE ƴᡈƍƱƖᲦƭǇǓ
ω12 = hg · v − hδ,Ω0= 2, K|VAL |1, K + hg,2= −eVg 2, K| exp{−2πig · (R + r)}|1, K + hg,(25)ưᩉᛦ δ ƕ‫ݱ‬ƞƍ଺ƷᲦ໯અѣཞ७ƷǨȍȫǮȸ(30)แˮǛ‫ ׋‬10(b) ƴᅆƢᲨǤǪȳƸɳᡶᢃѣ᣽ KǛᡲዓႎƴƱǔƜƱƕưƖǔƕᲦƦƷཞ७ƔǒưɨƑǒǕǔᲨƸȖȩȃǰӒ‫ݧ‬ƴ‫ࣖݣ‬Ƣǔᡞ఍‫܇‬șǯȈȫЎƷƜǕǑǓኒƷ‫׍‬ஊཞ७ᲦƢƳǘƪȉȬǹȈཞᢃѣ᣽‫҄٭‬ǛˤƏᢟᆆƷǈƕᚩƞǕǔᲨɥᚡƷ७ƸவˑɦᲢδ  1ᲣưƸᲦǤǪȳƕɥแˮưɳᡶᢃѣ᣽ K ư᫠ǜưƍǔཞ७ |2, K ƸᲦ|1, K+hg ƱǨȍȫǮȸƕǄǅ጑ᡚƠᲦƜƷᲬཞ७᧓ƴƸႻʝ˺ဇ VAL ƕ΁ƘᲨƜǕƸᡫࠝƷȉȬǹȈǢȈȠ
೉‫׹‬ƴƓƍƯᲦԈӓவˑɦư |2, N  Ʊ |1, N + 1

⎧
⎪
⎪
⎪
⎪
⎪
⎨

|+, K

⎪
⎪
⎪
⎪
⎪
⎩

|−, K

= sin |1, K + hg + eiα cos |2, K,= e−iα cos |1, K + hg − sin |2, K,(31)ƕ጑ᡚƢǔƜƱƴႻ࢘ƠƯƍǔᲨƜƷᲬแˮ᧓13‫ ׋‬11:ȉȬǹȈཞ७ |+, K ƷҾ‫܇‬Ʒඬѣ᧙ૠƷ଺᧓‫҄٭‬ᲦƓǑƼ g0,0,−2 ưਦ‫ܭ‬ƞǕǔҾ‫܇‬᩿ᲨƱᲬཞ७Ʒዴ࢟ኽӳƷ࢟ưࢽǒǕᲦฆӳᚌ Ƹ
tan 2 = −

|Ω0 |
,
δ

(32)

঺ЎǋਤƭƕᲦβ → 1 ƷಊᨂưƸήƱӷಮƴ್ඬƱƳǔᲨưɨƑǒǕǔᲨЎᘷƠƨȉȬǹȈཞ७Ʒɟ૾Ტ|+, KᲣƴƭƍ

ɟ૾ᲦRCE ᢅᆉƷЭࢸưλ‫ݧ‬ǤǪȳƷᢃѣ᣽ƯᲦඬѣ᧙ૠƷ࢟Ʒ଺᧓‫҄٭‬ƱᲦǫȃȗȪȳǰ

ƕᡞ఍‫܇‬șǯȈȫЎƩƚ‫҄٭‬ƠƯƍǔƜƱƴႸƴМဇƞǕƨ g0,0,−2 ưਦ‫ܭ‬ƞǕǔҾ‫܇‬᩿Ʒ᧙̞Ǜ˄ƚǔƱᲦƜǕƸ‫ׅ‬৵ྵᝋƷɟᆔưƋǔƱǋǛ‫ ׋‬11 ƴᅆƠƨᲨҾ‫܇‬᩿ǛʈǓឭƑǔԗ஖ưᚐ᣷ưƖǔᲨσᯚவˑ ΔE = hν ƱӷሁƷவˑp ཞ७Ʊ s ཞ७Ʒඬѣ᧙ૠƕฆӳᚌ ưฆơǓ

ƸᲦRCE ЭࢸƷλ‫ݧ‬ǤǪȳƷඬૠ kᲦӏƼ k − gӳƬƯƍǔᲨ˂૾Ʒ |−, K ǋӷಮưƋǔƕฆӳǛဇƍƯ
E(k) = E(k − g) + ΔE,ƷˮႻƕӒ᠃ƢǔƨǊƴඬѣ᧙ૠƷ࢟ƸɥɦǛ

(34)Ӓ᠃Ơƨ࢟ƱƳǔᲨƜƷǑƏƴƠƯࢽǒǕƨȉƱᘙƞǕᲦƜƷƱƖ |1, K+hg Ʊ |2, K ƷǨȍȫȬǹȈཞ७ƷǨȍȫǮȸ‫׍‬ஊ͌ƸǮȸƕ Brillouin zone ϋưʩࠀƠᲦϋᢿཞ७Ʒᢟ
K2hg · v(±)
E=+±  Ω20 + δ 2 , ų
2M2ᆆƕឪƜǔ [20]ᲨᡫࠝᲦቩ‫܇‬ዴƷ‫ׅ‬৵ྵᝋƸൔ᠋ႎȉȷȖȭǤඬᧈƕᧈƘඬѣࣱƕ᫋ᓸƱƳǔᩓ(33)‫܇‬ዴǍ༏ɶࣱ‫܇‬Ტ10−10 ∼ 10−12 mᲣƴƭƍƯᚇƱƳǓᲦ± Ʒ᪮ƴǑǓЎᘷǨȍȫǮȸƕࢽǒǕยƞǕǔƕᲦஜ᬴ܱưဇƍƯƍǔ᭗ǨȍȫǮȸǔᲨǇƨᲦƜǕǑǓؕࡁཞ७ 1

S Ɣǒ |+Ღ|−᣻ǤǪȳȓȸȠƷȉȷȖȭǤඬᧈƸ 2 × 10−16 mǁƷѕឪǨȍȫǮȸƸࡸ (17) ƷǑƏƴࢽǒǕ

Ტ200 ǢȈȡȸȈȫᲣƱಊᇢƴჺƍᲨƜƷǑƏǔᲨƜƷǑƏƴᲦȉȬǹȈǢȈȠ೉‫׹‬ƱӷơǢƳቩ‫܇‬ƴƓƍƯᲦඬƱƠƯƷࣱឋưƋǔ‫ׅ‬৵ྵȗȭȸȁư RCE ǛወɟႎƴᚡᡓƢǔƜƱƕư

ᝋƕឪƜƬƯƍǔƜƱƸᭃƖưƋǔᲨƩƕᲦኽƖǔᲨRCE ưƸᲦήѕឪƴƓƍƯǨȍȫǮȸƱ୒ƱƷႻʝ˺ဇƴƓƍƯᡞ఍‫܇‬șǯȈȫЎƷᢃᢃѣ᣽Ʒʩ੭ǛਃƏή‫܇‬ᲫƭƷࢫлǛᲦᡞ఍‫܇‬ѣ᣽ᆆᘍƷǈƕᚩƞǕᲦኳཞ७ƱƠƯƦƷǑƏ

șǯȈȫ g ƕௐƨƠƯƍǔƜƱƕЎƔǔᲨƜƷƳඬૠ‫҄٭‬Ʒ૝ʏඬƕƭǑƍࢍࡇǛǋƭᲦƱƍƱƖ g ƴ‫ࣖݣ‬Ƣǔᢃѣ᣽Ƹኽ୒ᢃѣ᣽ƱǋԠƹƏƷƸ‫ׅ‬৵ྵᝋƴ˂ƳǒƣᲦӞχᢃѣƢǔቩ‫܇‬ǕǔᲨܱᨥƷή‫܇‬ƸЎ૝᧙̞ E = pc Ǜǋƭ್ưƸឪƜǓƑƳƍƜƱưƋǔᲨƜǕƸɭမưஇඬưƋǔƷƴ‫ݣ‬ƠᲦƜƜưႇ‫ئ‬Ơƨ‫ڭڈ‬Ƴલ˩ǋჺƍඬᧈƷቩ‫܇‬ዴ‫ׅ‬৵ǛᚇยƠƨƜƱƴƳǔ

ή‫܇‬ƸᲦE = pcβ ƱƍƏήƱƸီƳǔЎ૝᧙̞ƱƱǋƴᲦ᭗ǨȍȫǮȸƷ᣻ǤǪȳƕඬƱƠƯǛਤƪᲦƞǒƴࡸ (7) ưᅆƞǕǔǑƏƴᲦጏඬƷˮႻǛ̬ƬƨǇǇ‫˳׍‬Ʒ೅ႎɶǛᡫᢅƠƯƍ

14ǔƱƍƏʙܱǋ‫ٻ‬ƖƘႺज़ƴӒƢǔᲨƱƜǖƕȄ GSI ƴƓƍƯᘍƍᲦLi ಮ U89+ ǤǪȳƷ 1s2 2sܱƸᲦƜƷᆉࡇƷǨȍȫǮȸ᪸؏ưƸᲦˮႻƕ- 1s2 2p3/2 ᢟᆆƷ RCE ǋᚇยƠƯƍǔ [21]Შʻ

‫҄٭‬ƢǔǑƏƳᘔᆳƷૺ᩿ᆢƸǤǪȳƷᡮࡇƱࢸᲦᔛᆢȪȳǰ ESR ƴƓƚǔǤǪȳȓȸȠƷᩓσƴถ‫ݲ‬ƢǔƨǊᲦƜƷǑƏƳྵᝋǛᚇยƢǔ‫܇‬ϬҲƳƲƱኵǈӳǘƤǔƜƱưǤǪȳȓȸȠƨǊƴƸஊМƴ΁ƘᲨǷȪǳȳኽ୒Ʒ఍‫᧓܇‬ᨠƷᡮࡇ࠼ƕǓǛ৮ƑᲦƞǒƳǔឬ᭗ЎᚐᏡЎήᆉࡇƴƓƚǔ 400 MeV/u Ar ǤǪȳƷ‫ׅ‬৵ᚌƸඥƱƠƯǋ‫᧏ޒ‬ƠƯƍƘʖ‫ܭ‬ưƋǔᲨ100 μrad ƷǪȸȀȸưƋǓᲦᡫࠝƷ૾ඥưƸܾତƴᚇยƠࢽƳƍƕᲦஜ৖ඥưƸ RCE ƱƍƏ

8. ᜓᠴᢅᆉǛʼƠƯᲦǤǪȳƷϋᢿཞ७ǛȗȭȸȖƱƠƯƜƷ‫ׅ‬৵ྵᝋƕᚇยƞǕƯƍǔᲨஜᄂᆮƸᓸᎍƷҦٟᛯ૨ƷȆȸȞƱƠƯி̢ᘍ૙੉Ʒਦ‫ݰ‬ƷǋƱᲦᡈᕲщᲦဣ‫ޛ‬ภᲦɶʟᨗ
ɟᲦ‫ݱ‬ཊᄂɟᢹᲦ‫߃ޛ‬඲ᙹӲ൞ƱƷσӷᄂᆮƴ

7. ǇƱǊƱʻࢸƷ‫᧏ޒ‬ƯᘍǘǕǇƠƨᲨƜƜƴขƘज़ᜓᐲƠǇƢᲨǇ
ƜƷǑƏƴᲦஜᄂᆮưƸᲭഏΨǳȒȸȬȳȈƨ᬴ܱǛᘍƏƴƋƨǓᲦಊǊƯ᭗ԼឋƷ᣻ǤǪσᯚѕឪƴƓƍƯ “͞ήƷСࣂ”Ʊ “Წ᣻σᯚ”ȳȓȸȠǛ̓ዅƠƯ᪬ƍƨ᭗ဋ௿ɟᲦ஭ɥͤɲ

ƱƍƏᲬƭƷǢǤȇǢǛ‫ݰ‬λƠƨᲨƜǕƴǑǓ

൞ǛƸơǊƱƢǔ્Ҕᄂ HIMAC Ʒ AEC ᬴ܱȬȸǶȸƷМဇƕ‫׉‬ᩊƳ X ዴ᪸؏ƴƓƍƯᲦҾǵȝȸȈǰȫȸȗᲦǪȚȬȸǿȸƷ૾ŷƴज़ᜓ‫܇‬ཞ७Ǜᐯ‫נ‬ƴǳȳȈȭȸȫƢǔƜƱƕưƖǔ

ƠǇƢᲨǑƏƴƳƬƯƖƨᲨƜǕƸᲦҥƴσᯚྵᝋƷᚇஜᄂᆮƸଐஜ‫ܖ‬ᘐਰᐻ˟ǑǓᅹᄂᝲؕႴ SᲦยƴƱƲǇƬƯƍƨࢼஹƷ 30 ࠰᧓ƷᄂᆮƱƸӏƼཎКᄂᆮՃ‫ڜ‬ѕᝲƷя঺ǛӖƚƯᘍǘǕǇЏǓӝƷီƳƬƨ RCE ᄂᆮƷૼƨƳ‫᧏ޒ‬ưƋƠƨᲨǓᲦჺඬᧈ᪸؏ƷҾ‫܇‬ཋྸƷႆ‫ޒ‬Ǜࢸ਀ƠƢǔࢍщƳȄȸȫƱƠƯ஖ࢳƕਤƯǔᲨӋᎋ૨ྂ̊ƑƹᲦRCE ǛМဇƠƯ He ಮǍ Li ಮƷ᣻ǤǪȳƷʚ᣻ѕឪǍɤ᣻ѕឪཞ७ᲦƢƳǘƪɶᆰ[1] V. V. Okorokov. JETP Lett., 2:111, 1965.

ǤǪȳǛᢠ৸ႎƴ˺ǔƜƱƴǋ঺ыƠƯƓǓᲦ[2] S. Datz, C. D. Moak, O. H. Crawford,ƜǕƸ˂Ʒ৖ඥưƸܾତưƸƳƍ ᲨƜƷǑƏ

H. F. Krause, P. F. Dittner, J. Gomez delƳǨǭǾȁȃǯƳҾ‫܇‬ƷನᡯǍߐْȀǤȊȟǯ

Campo, J. A. Biggerstaﬀ, P. D. Miller,ǹǛᛇኬƴᚇยƢǔƨǊƷ᬴ܱǛྵ‫נ‬แͳɶư

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ƋǔᲨRev. Lett., 40:843, 1978.

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ɟ૾ưЎήƱƠƯƷ᩿ͨƴႸǛӼƚǔƱᲦRCE[3] S. Datz, C. D. Moak, O. H. Crawford,ƴǑǔǨȍȫǮȸǹȚǯȈȫƸᲦኽ୒Ўή֥ư

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J. Gomez del Campo, J. A. Biggerstaﬀ,

ЎᚐᏡǛਤƬƯƍǔᲨƞǒƴȉȃȗȩȸ࠼ƕǓ

H. Knudsen, and P. Hvelpumd. Nucl. In-ǍǷȕȈƷࢨ᪪ǛӖƚƳƍᲦ‫ݲ‬᣽ƷǤǪȳưǋ

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јྙǑƘᚇยƕӧᏡưƋǔƳƲᲦЎή֥ƴ‫ݣ‬Ƣǔ

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M. Torikoshi, A. Kitagawa, E. Takada,ƠᲦҾ‫܇‬ఋᄂᆮǁƷࣖဇǋᙸᡂǊǔᲨƜƷǑƏƳ

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16

ǷȪȸǺ

ᘔᆳᛯȎȸȈ

IIIᲨ᩼࢐ࣱ૝ʏƩƚƕឪƜǔƜƱƸƳƍᲧ ්ள̬‫܍‬ƱȝȆȳǷȣȫƷᖎƱܱ Ყ޽஭ųѱྸ҄‫ܖ‬ᄂᆮ৑Ҿ‫܇‬ཋྸᄂᆮܴ
shimamur@ribf.riken.jp
࠯঺ 22 ࠰ 8 உ 19 ଐ ҾᆜӖ˄

1

ƸơǊƴ

ȝȆȳǷȣȫ‫ئ‬ƴǑǔ૝ʏƷ᣽‫܇‬ᛯǛИǊƯ‫ܖ‬ǜƩƱƖᲦ૝ʏඬѣ᧙ૠƷ๴ᡈ࢟

ψ(r) r→∞−→ exp(ikz) + f (θ, φ) exp(ikr)/r(1)

ƴᲦႏƞǜᲦƢƙƴኛࢽưƖƨưƠǐƏƔᲨ૝ʏƕƳƚǕƹᇹ 1 ᪮Ʒλ‫࠯ݧ‬᩿ඬƩƚƴƳǓǇƢᲨ૝ʏƕឪƜǔƱᇹ 2 ᪮Ʒྶ᩿ඬƕဃǇǕᲦƦƷਰࠢ f (θ, φ) ƴǑǓࣇЎૺ᩿ᆢƕ |f |2 ƱᘙƞǕǔƱ૙ǘǓǇƢᲨưǋᲦ૝ʏƕឪƜƬƯǋ࠯᩿ඬƷਰࠢƸถǓǇƤǜᲨƍƬƨƍ૝ʏඬƸƲƜƔǒิƖЈƨƷưƠǐƏᲨλ‫ݧ‬ඬƷɟᢿƕ࢐Ɩ᫠ƹƞǕƨƷƕ૝ʏඬƳƷưƸƳƍưƢƔᲨ࢐Ɩ᫠ƹƞǕƨЎƩƚλ‫ݧ‬ඬƸਰࠢƕЪǓӕǒǕƯƠƔǔǂƖưƸƋǓǇƤǜƔᲨƜǕƸቩ‫܍̬܇‬Ʒբ᫆ƱਵƑǔǂƖưƠǐƏᲨƠƔƠᲦ૝ʏྸᛯưƸቩ‫܇‬፭Ʒ්ǕǛඬѣ᧙ૠƕᘙƠᲦቩ‫܇‬ૠ̬‫܍‬ƴႻ࢘ƢǔಒࣞƸᄩྙƷ්ǕƷ݅ࡇᲦ්ள (ȕȩȃǯǹ ﬂux) Ʒ̬‫܍‬ƱƍƏ࢟ǛӕǓǇƢᲨ්ளᲦȕȩȃǯǹƸƋǔ᩿Ǜ‫׶‬Ⴚƴ್Џǔቩ‫܇‬Ღឋ᣽ᲦǨȍȫǮȸƳƲƷ්ǕǛҥˮ଺᧓Ღҥˮ᩿ᆢ࢘ǓƷࢍƞưᘙƠƨǋƷưƢᲨȝȆȳǷȣȫ‫ئ‬ƴǑǔ૝ʏưƸ࢐ࣱ૝ʏƠƔឪƜǓǇƤǜᲨƠƔƠᲦɟᑍƷᘔᆳᢅᆉưƸǨȍȫǮȸவˑƕᚩƤƹ᩼࢐ࣱ૝ʏǋឪƜǓࢽǇƢᲨƢǔƱλ‫ݧ‬ȓȸȠƸ࢐ࣱ૝ʏ঺ЎᲦ᩼࢐ࣱ૝ʏ
঺ЎᲦ᩼૝ʏ঺ЎƷɤƭƴЎƔǕǇƢᲨƜǕǒƷ්ளƷዮԧƕλ‫්ݧ‬ளƴሁƠƚǕƹᲦƲǜƳЎƔǕ૾ǛƠƯǋನǘƳƍƸƣưƢᲨƱƜǖƕᲦ᩼࢐ࣱ૝ʏƕឪƜǔƱƖƴƸ࢐ࣱ૝ʏƕൿƠƯǼȭƴƳǒƳƍᲦǼȭƳǒ්ள̬‫܍‬ЩƕᄊǕǔᲦ

17ƱƍƏɧ࣬ᜭƳʙܱƕƋǓǇƢ (ᇹ 2 ራ)Შ
්ள̬‫܍‬Ƹ࣏ƣ঺ǓᇌƭƷưƠǐƏƔᲹ̊ƑƹᲦᨗᩓ‫܇‬Ƹᩓ‫܇‬ƱᢙᢀƢǕƹ‫ݣ‬ෞ๒ƠƯƠǇƍǇƢᲨƦƏƢǕƹᲦᨗᩓ‫܇‬ᘔᆳưλ‫ݧ‬ᨗᩓ‫܇‬ȓȸȠƷ්ளƸ̬‫܍‬ƞǕǇƤǜᲨᨗᩓ‫܇‬ෞ๒Ƹ᩼Ⴛ‫ݣ‬ᛯႎ᣽‫܇‬ᛯƷྵᝋưƸƳƍƷƩƔǒᲦǷȥȬȸȇǣȳǬȸ૾ᆉࡸưᘙƤƳƍƷƸ࢘ǓЭƱƍƏƜƱưƠǐƏƔᲨ්ள̬‫܍‬ЩǛྸᛯႎƴ‫ݰ‬ƘƴƸᲦ˴ƔЭ੩வˑƕ࣏ᙲưƠǐƏƔᲨƦƷவˑǛ૏ॖƴᄊƬƯǈƨǒᲦૼƠƍƜƱƕᙸƑƯƜƳƍưƠǐƏƔᲨ̊ƑƹᲦᨗᩓ‫܇‬ෞ๒ǛǷȥȬȸȇǣȳǬȸ૾ᆉࡸƷ௒ϋưᘙƤƳƍưƠǐƏƔᲨʻ‫ׅ‬ƸᲦƜǕǒ්ள̬‫܍‬ЩƴǇƭǘǔƍƘƭ
ƔƷᛅ᫆ǛӕǓɥƛǇƢᲨ

2᩼࢐ࣱ૝ʏƸ࢐ࣱ૝ʏǛˤƏˮፗࡈ೅ r ƷѣࢲᢿЎƴƠƔ̔ǒƳƍᲦྶ‫ݣ‬ᆅȝȆȳǷȣȫƴǑǔ૝ʏǛᎋƑǇƢᲨᚌࡇ૾ӼƷщƕ΁ƔƳƍƷưᚌᢃѣ᣽᣽‫܇‬ૠ l Ƹ̬‫܍‬ƞǕᲦƦǕƧǕƷᢿЎඬ l ƸǄƔƷᢿЎඬƱฆơǓǇƤǜᲨӲѣࢲඬѣ᧙ૠƸ๴ᡈ࢟φl (r) r→∞−→ sin(kr − lπ/2 + δl )∝ e−i(kr−lπ/2) − Sl e+i(kr−lπ/2)(2)ǛǋƪǇƢ [1–4]ᲨƜƜư δl Ƹ૝ʏƴǑǔˮႻƷƣǕᲦǇƨ Sl = exp(2iδl ) ưᲦƜǕǛ૝ʏᘍЗᲦS ᘍЗƱԠƼǇƢᲨࡸ (2) ƴǑǕƹᲦS ᘍЗƷཋྸႎॖԛƸᲦҥˮਰࠢƷϋӼƖྶ᩿ඬ e−i(kr−lπ/2)ƕᢒƘƔǒ૝ʏɶ࣎ƴӼƔƬƯλƬƯƖƨƱƖᲦɶ࣎ưៃƶᡉƞǕᲦᢒƘǁЈƯᘍƘ‫ٳ‬ӼƖྶ᩿

3

ඬ e+i(kr−lπ/2) ƷਰࠢƱᚕƑǇƢᲨ૝ʏƕឪƜǒƳƚǕƹ δl = 0 ưᲦSl = 1 ưƢƔǒᲦSl Ʒ 1 ƔǒƷƣǕƕ૝ʏјௐǛᘙƠǇƢᲨܱᨥᲦᢿЎඬ૝ʏਰࠢƸ Sl − 1 ƴൔ̊ƠᲦᢿЎඬૺ᩿ᆢ σl Ƹ|Sl − 1|2 ƴൔ̊ƠǇƢᲴσl ∝ |Sl − 1|2 = 4 sin2 δl .

(3)Sl Ʒ‫ܭ‬፯Ɣǒ |Sl | = 1 ưƋǔƜƱƸଢǒƔưᲦϋӼƖඬƷਰࠢƷዌ‫ ͌ݣ‬2 ʈƱ‫ٳ‬ӼƖඬƷƦǕƱƸሁƠƘᲦƜǕƸྶ‫ݣ‬ᆅ‫ئ‬ƴǑǔҥኝƳ૝ʏưƸӲᢿЎඬƷ්ளƕ̬‫܍‬ƞǕǔƜƱǛᅆƠƯƍǇƢᲨƠƔƠᲦǋƠǋ᩼࢐ࣱ૝ʏƕឪƜǕƹᲦƦƷȁȣȍȫƴ්ளƷɟᢿƕ‫ڞ‬ǘǕᲦ|Sl | < 1 ƱƳƬƯƠǇƍǇƢᲨƦǜƳ Sl Ƹዌ‫ݣ‬ƴ Sl − 1 ǛǼȭƴưƖǇƤǜᲨƭǇǓᲦࡸ (3) Ʒ σl ǛǼȭƴưƖǇƤǜᲨ᩼࢐ࣱ૝ʏƕឪƜǔƳǒ࣏ƣ࢐
ࣱ૝ʏǋឪƜǒƳƚǕƹƳǒƳƍƱƍƏ᣽‫܇‬ᛯјௐƕᲦƜƏƠƯቇҥƴᅆƤǇƢᲨ᩼࢐ࣱ૝ʏƷǇƱǋƳৢƍᲦዬ݅ኽӳඥᲦȁȣȍȫኽӳඥǛƝ‫܍‬ơƷ૾ƸƜǕƴီᛯƕƋǔƔǋჷǕǇƤǜᲨ࢐ࣱ૝ʏƠƔৢƑƳƍȝȆȳǷȣ
ȫ૝ʏྸᛯǛ̅ƍᲦࢍࡽƴ |Sl | < 1 ƱƢǔƜƱư
᩼࢐ࣱ૝ʏјௐǛӕǓλǕƨƾǓǛƠƯƍǔƩ
ƚƴᙸƑǔƔǒưƢᲨưǋᲦƜǕƕദƠƍᎋƑ૾ưƋǔƜƱƸˌɦƷǑƏƴƠƯЎƔǓǇƢᲨȁȣȍȫ᧓ƷኽӳƸҥˮਰࠢƷϋӼƖඬƕλǔȁȣȍȫ i ƱƸКƷȁȣȍȫ j ƴ‫ٳ‬ӼƖඬǛဃǈᲦƦƷਰࠢǛ Sji ƱƢǕƹ‫ٶ‬ȁȣȍȫ S ᘍЗƷᇹ i З Sji (j = 1, 2, · · ·) Ǜ‫ܭ‬፯ưƖǇƢᲨȁȣȍ
ȫ i ƴλƬƨ්ளƕ̬‫܍‬ƞǕǔƴƸ j |Sji |2 =1
ưƳƚǕƹƳǓǇƤǜᲨ᩼࢐ࣱȁȣȍȫ j = i ƴਰࠢƕǼȭưƳƍ‫ٳ‬ӼƖඬƕɟƭưǋƋǕƹᲦ࣏ƣ |Sii |2 <1 Ǜ฼ƨƠǇƢᲨSii Ƹྶ‫ݣ‬ᆅ‫ئ‬ưƷ Sl ƱӷơƘϋӼƖඬƷȁȣȍȫƴЈƯᘍƘ‫ٳ‬ӼƖඬƷਰࠢǛᘙƢƷưᲦ࢐ࣱ૝ʏૺ᩿ᆢ σel Ƹ|Sii − 1|2 ƴൔ̊ƠᲦσel > 0 ƴƳǔƷưƢᲨဏࣱငҳƩƬƯ

᩼ဏࣱငҳƕ
ƋǔƱƖƸዌ‫ݣ‬ƋǔᲛ18ย‫ܭ‬ɧᏡƳᄩྙ්ளƷ̬‫܍‬Щឋ᣽ m Ʒቩ‫܇‬ƴƭƖᲦᢃѣ᣽șǯȈȫ๫ም‫܇‬p̂ = −ih̄∇ ƱᡮࡇƷǑƏƳ๫ም‫ ܇‬v̂ = p̂/mᲦᢃѣǨȍȫǮȸ๫ም‫ ܇‬T̂ = p̂2 /2m = −(h̄2 /2m)ΔᲦȝȆȳǷȣȫ V (r, t)ᲦȏȟȫȈȋǢȳ Ĥ ǛৢƍǇƢᲨ଺᧓̔‫܍‬ǷȥȬȸȇǣȳǬȸ૾ᆉࡸ∂Ψ= ĤΨ = (T̂ + V )Ψ
(4)
ih̄
∂t
Ǜ฼ƨƢඬѣ᧙ૠΨ(r, t)ƔǒൿǇǔʚƭƷ᣽Ღ

P (r, t) = |Ψ(r, t)|2 Ღ(5)j(r, t) = (Ψ∗ v̂Ψ − Ψv̂Ψ∗ )/2(6)ǛᎋƑǇƢᲨP (r, t) Ƹᄩྙ݅ࡇƴൔ̊ƠᲦ˳ᆢƷᡞૠƷഏΨǛǋƪǇƢᲨj(r, t)ǛોǊƯ්ளƱԠƼǇƠǐƏᲨᄩƔƴ [ᡮࡇ]/[˳ᆢ] ƷഏΨǛǋƪᲦҥˮ଺᧓Ღҥˮ᩿ᆢ࢘ǓƷ᣽ưƢᲨƜǕƕƳƥ්ளƱᚕƑǔƷƔᛟଢƤƣƴ̅ƬƯƍǔ૝ʏƷ૙ᅹ୿ǋƋǓǇƢƕ [1, 2]ᲦƦǕƸ᣽‫܇‬ᛯሁƷ૙ᅹ୿ƴඬѣ᧙ૠƷཋྸႎᚐ᣷ƴ᧙ᡲƠƯᲦ්ǕƷ̬‫܍‬ЩƱƱǋƴᛟଢƞǕƯƍǇƢ [3–5]Შ
Ƌǔᆰ᧓ V ϋƷμᄩྙƷ଺᧓‫҄٭‬ǛᛦǂǇƢᲨ૾ᆉࡸ (4) ƴǑǓ Ψ Ʒ଺᧓ࣇЎǛȏȟȫȈȋǢ
ȳƷ๫ምƴፗƖ੭ƑǔƜƱƕưƖᲦ


 
∂
∂Ψ
∂Ψ∗
+Ψ
P (r, t) dr =
Ψ∗
dr
∂t V
∂t
∂t
V


= −(i/h̄) [Ψ∗ (ĤΨ) − Ψ(ĤΨ)∗ ] dr
V

= QT (t) + QV (t).

(7)ƜƜư QV (t) ƸȝȆȳǷȣȫ V ƴ̔ǔᢿЎQV (t) = −(i/h̄) [Ψ∗ (V Ψ) − Ψ(V Ψ)∗ ] drV

= (2/h̄) (Im V )P (r, t) drV(8)ưƢᲨV Ƹܱૠ᧙ૠưƢƔǒᲦƦƷᖎᢿ Im V Ƹ࢘໱ǼȭᲦƠƨƕƬƯ QV (t) ǋǼȭưƢᲨᢃѣǨȍȫǮȸ๫ም‫ ܇‬T̂ ƴ̔ǔᢿЎ QT (t) Ǜ˄᥵ư‫࢟٭‬ƠƨኽௐƷࡸ (A.2) Ǜࡸ (7) ƱൔǂǕƹᲦᘮᆢЎ᧙ૠӷٟƷഏƷሁࡸǛࢽǇƢᲴ∂P (r, t) = −∇· j(r, t).
(9)∂tƜǕƸิƖЈƠǋԈƍᡂǈǋƳƍ݅ࡇ P Ღ්ளj Ʒ්˳ưƷᑣƘჷǒǕƨᡲዓƷ૾ᆉࡸᲦ්ǕƷ̬‫܍‬ЩƱӷơ࢟ǛƠƯƍǇƢᲨƦƜư j ǛᄩྙƷ්ளșǯȈȫᲦᄩྙƷ්ǕƷ݅ࡇ (probability
current density) Ʊᚐ᣷ưƖǔưƠǐƏ [3–5]Შ

ƷƔᲨƜǕǛᛦǂǔƨǊᲦ๴ᡈ࢟ (1) Ǜ්ள j(r)Ʒࡸ (6) ƴˊλƢǔƱᲦኽௐƸ 3 ঺ЎƴЎƔǕǇƢᲨΨ(r, t)ᲦΨ∗ (r, t)ƷᲦƭǇǓψ(r)Ღψ ∗ (r)Ʒλ‫ݧ‬ඬᢿЎƩƚƔǒဃơǔ j in (r)Ღ૝ʏඬƩƚƴǑǔ j sc (r)ᲦƦƠƯɲ૾ƷඬƷ࠮ฏ᪮ j int (r) ưƢᲨj in (r) Ƹ࠯᩿ඬƷᡶᘍ૾ӼǛӼƘҥˮ˳ᆢ࢘Ǔ‫ٻ‬Ɩƞ v *1) ƷșǯȈȫƴƳǓǇƢᲨ‫ٻ‬ƖƳҞࢲr Ʒྶ᩿ S ɥǛඥዴ૾ӼƴЈǔ j sc (r) Ʒѣࢲ঺Ў
jrsc (r) ƸᲦr Ʒ᝟ǂƖ r−n Ʒ᭗ഏ᪮Ǜ໯ᙻƢǔƱƨƩᲦᄩྙ݅ࡇ P (r, t) ƱᢌƍᲦ්ள j(r, t) ƸദᄩƴยǕƳƍ᣽ưƢ [4]Შj(r, t) ǛൿǊǔƴƸˮፗƱᢃѣ᣽Ǜӷ଺ƴദᄩƴൿǊƶƹƳǒƣᲦɧᄩ‫ࣱܭ‬ҾྸƴӒƢǔƔǒưƢᲨưǋᲦ්ளƕˮፗƷ‫҄٭‬ƱƱǋƴǏƬƘǓƱƠƔ‫٭‬ǘǒƳƚǕƹ
җЎƳችࡇưย‫ܭ‬ưƖǔưƠǐƏᲨj(r, t) ƕ්ளƷॖԛǛǋƭƴƸƜƷவˑƕ࣏ᙲưƢᲨȏȟȫȈȋǢȳƕǨȫȟȸȈƩƱƢǔƱࡸ(7)Ღᇹ 2 ᘍƷᆢЎƸࠝƴǼȭưƢᲨƜǕƕ‫ٻ‬᧓ᢌƍưƋǔƜƱƸЭ‫ׅ‬ᛇƠƘᡓǂƨᡫǓưƢᲨƜƷᆢЎƸЭ‫ׅ‬Ღ˄᥵ B ưৢƬƨѣࢲ᧙ૠφ∗ ψ  − φ∗ ψ ƷᆢЎƴ˩ƯƍǇƢᲨƦƜưᅆƠƨᆢЎࠀǛᘙ᩿᪮ưᘙƢ৖ඥǛ˳ᆢᆢЎƴ໲ƖႺƤƹᚘምưƖǇƢᲨƭǇǓᲦᢿЎᆢЎƴǑǓ˳ᆢᆢЎǛᘙ᩿ᆢЎƴ‫٭‬ƑǔǰȪȸȳƷ‫ྸܭ‬Ǜ˄᥵Ღࡸ (A.2) ƷӫᡀƴᢘဇƢǕƹ
∂
P (r, t)dr = − j n (r, t)dS
(10)
∂t V
S
ǛࢽǇƢᲨӫᡀƷᆢЎƸ᪸؏ V Ǜ‫׊‬ǉᘙ᩿ S μ˳ƴʠǓᲦj n ƸӲ᩿ᆢእ༾ dS ƴᇌƯƨ‫ٳ‬ӼƖඥዴ૾ӼƷșǯȈȫ j(r, t) Ʒ঺ЎưƢᲨӫᡀƷ᝟ӭƴදॖƢǕƹᲦᘙ᩿ S ǛᡫƬƯ᪸؏ V ƴλƬƯƘǔദԛƷμ්ளƕ V ϋƷ‫נ܍‬ᄩྙƷ‫ف‬ьྙƴሁƠƍƱƍƏᄩྙƷ්ǕƷ̬‫܍‬ЩǛࡸ (10) ƸᘙƠǇƢᲨƜǕƱӷሁƳࡸ (9) ǋ්ǕƷ̬‫܍‬ЩǛॖԛƢǔƜƱƸᲦɥưᡓǂƨᡫǓưƢᲨȝȆȳǷȣȫ V ƕ଺᧓ƴ̔ǒƳƚǕƹᲦඬѣ૾ᆉࡸ Ĥψ(r) = Eψ(r) Ǜ฼ƨƢ ψ(r) ƴؕƮƘΨ(r, t) = ψ(r)e−iEt/h̄

jrsc (r) = (v/r2 )|f (θ, φ)|2 .

ࣇ‫ݱ‬ᇌ˳ᚌ dω Ǜᙸᡂǉ S ɥƷ᩿ᆢ r2 dω Ǜᡫǔ්
Ǖ v|f |2 dω Ǜ |j in |ưлƬƨ |f |2 dω ǛᲦᇌ˳ᚌ dω࢘ǓƷࣇЎૺ᩿ᆢ dσ ƱʖेưƖǇƢᲨưǋᲦ࠮ฏ᪮ǋƋǓǇƢᲨƦƷѣࢲ঺Ў jrint (r) Ƹjrint (r) = (v/r)(1+χ) Re [f (θ, φ)eikr(1−χ) ] (13)ƕɼᙲ᪮ưƢ [1–3]ᲨƜƜư χ = cos θ ᲦǇƨ Re ƸܱᢿƷॖԛưƢᲨਦૠ᧙ૠƷᏅƸኝᖎૠư‫ٻ‬ƖƳ r ƕƔƔǓᲦθ ƕǘƣƔƴѣƍƯǋ jrint (r) ƸນƠƘਰѣƠᲦ්ளƷॖԛǛ‫ڂ‬ƍǇƢᲨƦǕǛൔ᠋ႎ཰ƍ θ Ʒር‫׊‬ư࠯‫ר‬ƠƯǋǼȭưᲦƜǕƸ໯ᙻưƖǇƢᲨ̊‫ٳ‬Ƹ kr(1 − χ) ƕ‫ٻ‬ƖƘƳƍƱƖᲦƭǇǓ θ ƕƝƘ‫ݱ‬ƞƍƱƖƩƚưƢᲨ࠯᩿ඬƱྶ᩿ඬƷ࠮ฏƕ θ  0 ưƠƔឪƖƳƍƷƸᲦ࠯᩿ඬƕЭ૾ (θ = 0) ƴƠƔЈƳƍƔǒưƢᲨኽ‫ޅ‬Ღ࠮ฏ᪮Ǜ໯ᙻƠƯ jrsc Ʊ |j in | ƩƚƔǒࣇЎૺ᩿ᆢǛЈƠƨࡸ (12) ƷɦƷᎋƑƸᲦθ  0 Ǜᨊƚƹբ᫆ƋǓǇƤǜᲨ࠯᩿ඬƸദᄩƴ θ =0 ƴƠƔЈƳƍƷƴᲦƳƥ࠮ฏƕƦƷᡈᡀƷ θ ưǋឪƜǔƷưƠǐƏᲨλ‫ݧ‬ȓȸȠƷ‫ٽ‬ƞƕஊᨂƳǒƹᲦǘƣƔưǋ୺ƛǒǕƨ૝ʏඬƸҗЎᢒƘưƸȓȸȠƔǒƦǕƯ
࠮ฏƸෞƑǇƢᲨƠƔƠᲦ࠯᩿ඬƸ໯ᨂƴ‫ٽ‬ƘᲦμᆰ᧓ǛҩǊǔƷưᲦ૝ʏඬƕƍƔƴᢒƘǁᘍƜƏƱᡜǕǒǕƣᲦ࠮ฏƕឪƜǔƷưƢᲨ࠮ฏ᪮ (13) ƕ θ  0 (χ  1) ƩƚưјƘƷƳǒ
1 + χ Ƹ 2 ƴᲦf (θ, φ) Ƹ (θ → 0 ưஊᨂƳǒƹ)f (θ =0) ƴፗƖ੭ƑǒǕᲦྶ᩿ S ƔǒЈǔ්ளƸ

(11)Ƹ଺᧓̔‫܍‬ǷȥȬȸȇǣȳǬȸ૾ᆉࡸ (4) Ǜ฼ƨƢƜƱƕᲦih̄∂e−iEt/h̄ /∂t = Ee−iEt/h̄ ƔǒЎƔǓǇƢᲨƜƷƱƖ P (r, t) = |ψ(r)|2 ưᲦ଺᧓ƴ̔ǒƳƍ‫ࠝܭ‬᣽ƴƳǔƷưᲦࡸ (9) ǋ (10) ǋɲᡀƱǋǼȭưƢᲨƲǜƳᆰ᧓᪸؏ưǋᲦƦƷɶƴλǔ්ளƱƦƜƔǒЈǔ්ளƸࠝƴ࠯ᘖǛ̬ƪᲦࠀƠࡽƖǼȭƱƍƏƜƱưƢᲨඬѣ᧙ૠ (11) Ʒ଺᧓‫܇׆‬Ƹ්ளƷࡸ (6) ưǋෞƑᲦΨ(r, t) Ǜ ψ(r)ƴፗƖ੭ƑƯǑƘᲦj(r, t) Ǜ j(r) Ʊ୿ƚǇƢᲨ

4



S

λ‫ݧ‬ඬƔǒᡜǕǒǕƳƍ૝ʏඬjrint (r)dS = −(4πh̄/m) Im f (θ = 0),(14)ǇƨᲦ૝ʏ᪮ (12) ƴƭƍƯƸഏࡸƴƳǓǇƢᲴஇИƷွբƴ৏ǓǇƠǐƏᲨ૝ʏඬƸƲƜƔǒิƖЈƨƷƔᲦƦǕƸ්ள̬‫܍‬ЩǛᄊǒƳƍ
*1)

(12)



S

jrsc (r)dS = v |f (θ, φ)|2 dω = (h̄k/m)σ. (15)ᢃѣ᣽Ǜឋ᣽ưлƬƨ h̄k/m ǛˌɦᲦv Ʊ୿ƍƯᡮࡇǛᡲेƢǔƜƱƴƠǇƢᲨ

19଺᧓᩼̔‫܍‬ȝȆȳǷȣȫƷ‫ئ‬ӳᲦƲǜƳᆰ᧓ưƋǕᲦЈλǓƢǔ්ளƸƭǓӳƍᲦദԛǼȭƩƱƍƏ̬‫܍‬ЩǛɟᑍЩƱƠƯЭራưᅆƠǇƠƨᲨɟಮƳλ‫්ݧ‬ள j in (r) ƩƚƳǒଢǒƔƴƜƷ̬‫܍‬ЩǛ฼ƨƢƷưᲦྶ᩿ S Ǜᡫǔμ˳Ʒ්ளƷЈλǓƕƭǓӳƏƴƸᲦ࠮ฏ᪮ (14) Ʊ૝ʏ᪮ (15)Ƹ৙ƪෞƠӳǘƶƹƳǓǇƤǜᲨƭǇǓᲦׄ૾ο૾ǁ૝ʏƞǕǔ්Ǖ (15) ƷЎƩƚᲦθ  0 Ʒ᝟Ʒ࠮ฏ᪮ (14) Ʒ࢟ưλ‫්ݧ‬ளƕЪǓӕǒǕƯƍǔ
ƷưƢ [1–4]Შࡸ (14)Ღ(15) ƷƜƷ᧙̞Ɣǒσ = (4π/k) Im f (θ = 0)(16)ƕࢽǒǕǇƢᲨƜǕǛή‫ྸܭܖ‬ƱԠƼǇƢᲨྶ‫ݣ‬ᆅ‫ئ‬ưƷή‫ྸܭܖ‬ƸᲦμૺ᩿ᆢ σ Ʊ૝ʏਰࠢ f (θ) ǛᢿЎඬƝƱƴ δl ưᘙƢࡸǛൔǂǕƹᄩᛐưƖǇƢ [1–4]ᲨƠƔƠᲦƦǕƩƚưƸҥƳǔૠࡸ᧓Ʒ᧙̞ƴᢅƗǇƤǜᲨƦƷ᧙̞ƕǑǓɟᑍႎƳ්ள̬‫܍‬ЩƔǒᐯ໱ƴЈǔƱƍƏཋྸႎྸᚐƕ‫ٻ‬ЏưƢᲨ᩼࢐ࣱ૝ʏǍӒࣖƕឪƜǔ‫ئ‬ӳưǋᲦμᢅᆉƷૺ᩿ᆢƷዮԧǛࡸ (16) Ʒσ ƱƠᲦ࢐ࣱ૝ʏਰࠢǛ f (θ) ƱƠƨɟᑍ҄ή‫ܖ‬‫ྸܭ‬ƕᲦӷơ්ள̬‫܍‬ƷᎋƑƔǒ‫ݰ‬ƚǇƢᲨǇƨᲦЭ૾ (࢐ࣱ) ૝ʏਰࠢƷᖎᢿƕ࣏ƣദƴƳǔƜƱǋ (ɟᑍ҄) ή‫ྸܭܖ‬ƔǒႺƪƴЎƔǓǇƢᲨƱƜǖưᲦࡸ (2)Ღᇹ 2 ᘍǛࡸ (6) ƴˊλƢǔƱᲦϋӼƖඬƷ්ளƸ v Ღ‫ٳ‬ӼƖඬƷ්ளƸ v|Sl |2 ᲦɲᎍƷ࠮ฏƸǼȭưᲦ්ள (6) Ǜ‫ݰ‬λƢǔЭƷᇹ
2 ራƷᜭᛯƕ‫࢘ڲ‬ưƋƬƨƜƱƕЎƔǓǇƢᲨ5

VIm ∝ i δ(ri ) ưƢᲨƨƩƠᲦࡸ (17) Ʒ ψ Ƹᨗᩓ‫܇‬-೅ႎኒμ˳Ʒඬѣ᧙ૠƴƳǓǇƢᲨV ƕᙐእ᣽ƳǒȏȟȫȈȋǢȳƸ᩼ǨȫȟȸȈưᲦƦƷ‫׍‬ஊǨȍȫǮȸǋᙐእૠưᲦƦǕǛ̊
Ƒƹ Er − iΓ/2 Ʊ୿ƚƹ Γ ƸƦƷཞ७ƷǨȍȫǮȸƷƋƍǇƍƞᲦh̄/Γ ƕ‫ݤ‬ԡǛᘙƠǇƢᲨƦƜư VIm Ǜ̅ƍᲦ̊ƑƹȝǸȈȭȋǦȠ (ᩓ‫܇‬-ᨗᩓ‫܇‬ளጉኒ) Ʒ‫ݤ‬ԡǛᚘምưƖǇƢᲨܱƸᲦᙐእǨȍȫǮȸཞ७Ƹ᩼ཋྸႎƳˎेཞ७ưᲦƦƷඬѣ᧙ૠƸᢒ૾ưႆ૝ƠǇƢᲨྵܱƷཋྸႎཞ७ƱƷ᧙̞ƴƭƍƯƸКᆜǛƝᚁƘƩƞƍ [6]Შ᩼࢐ࣱ૝ʏǍӒࣖƴǑǓ࢐ࣱ૝ʏȁȣȍȫƔ
ǒ්ளƕ‫ڂ‬ǘǕǔјௐƸᲦȝȆȳǷȣȫ‫ئ‬ƴǑǔ૝ʏƷྸᛯƴ VIm Ǜ‫ݰ‬λƢǕƹ࢟ࡸႎƴᘙƤᲦƦƷૺ᩿ᆢƕࡸ (17) ƔǒࢽǒǕǇƢᲨȝȆȳǷȣ
ȫƕᙐእ᣽Ƴǒѣࢲඬѣ᧙ૠǋˮႻƷƣǕ δl ǋᙐእ᣽ƴƳǓᲦ|Sl |=| exp(2iδl )|<1 ƱƳǔƷưᲦᇹ 2 ራЭҞƷᜭᛯƕᑣƘྸᚐưƖǇƢᲨ˄᥵Ჴ ᄩྙƷ‫҄٭‬ᡮࡇஜ૨Ღࡸ (7) Ʒ QT (t) ƸᲦ๫ም‫܇‬ƷࣱឋƴǑǓ−i[Ψ∗ T̂ Ψ − ΨT̂ Ψ∗ ] dr
h̄ V

−i
[Ψ∗ p̂2 Ψ − Ψp̂2 Ψ∗ ] dr=
2mh̄ V−ip̂ · [Ψ∗ v̂Ψ − Ψv̂Ψ∗ ] dr (A.1)=
2h̄ V

QT (t) =Ʊ‫࢟٭‬ƞǕǇƢᲨ‫ٻ‬ਙࢆϋƸࡸ (6) Ʒ්ளșǯȈȫ j(r, t) Ʒ 2 ̿ƳƷưഏࡸƕ‫ݰ‬ƚǇƢᲴᙐእȝȆȳǷȣȫƱ්ள̬᩼‫܍‬ཋྸႎƳȝȆȳǷȣȫ V ƸܱૠƩƔǒࡸ (8)Ʒ QV (t) ƸǼȭƩƱƠƯ්ள̬‫܍‬Щ (9)Ღ(10) Ǜ‫ݰ‬ƖǇƠƨᲨƠƔƠᲦˎƴ V ƴᖎᢿƕƋǕƹᲦࡸ(10) Ʒӫᡀƴࡸ (8) ƕᲦǇƨࡸ (9) ƷӫᡀƴǋӷಮƳ᪮ƕьǘǓᲦ̬‫܍‬ЩƕᄊǕǇƢᲨƭǇǓᲦʴໝႎƴᖎᢿ VIm ǛλǕǕƹᲦ්ளƷဃ঺ (VIm > 0)Ღ
Ԉӓ (ෞ๒)(VIm < 0) ǛᘙƤǔưƠǐƏᲨVIm ƴǑǔԈӓૺ᩿ᆢǛ σabs ƱƢǕƹ්ள੷‫ڂ‬ȬȸȈ −QV Ƹ |j in |σabs ƳƷưᲦඬѣ᧙ૠ ψƕҥˮਰࠢƷλ‫࠯ݧ‬᩿ඬǛǋƯƹᲦࡸ (8) ƴǑǓσabs = −QV /|j in | = −(2/h̄v)(ψ, VIm ψ) (17)Ʊ୿ƚǇƢᲨᨗᩓ‫܇‬ᘔᆳưƸᲦᨗᩓ‫܇‬ෞ๒Ƹ೅ႎϋӲᩓ‫܇‬ƱƷុᩉ ri ƕǼȭƷƱƖƴឪƜǔƷưᲦ

20

QT (t) = −V∇· j(r, t)dr.

(A.2)[1] ჿ߷᣻̮Ღ૝ʏƷ᣽‫܇‬ᛯᲦ‫ޥ‬ඬ୿ࡃ (1977).
[2] ᭗௶ԧ‫پ‬Ღᩓ‫܇‬ȷҾ‫܇‬ȷЎ‫܇‬ƷᘔᆳᲦؔ᫘᫾
(1972, ોᚖ༿ 1996).
[3] B. H. Bransden and C. J. Joachain, Physics
of Atoms and Molecules (Pearson Education,
Harlow, 1983, 2nd ed. 2003) (ȚȸȑȸȐȃǯ:Longman, Prentice Hall).
[4] L. I. Schiﬀ, Quantum Mechanics, 3rd ed.
(McGraw-Hill, N.Y., 1968). ǷȃȕᲦ᣽‫܇‬щ‫ܖ‬(ᢰᚪ)ᲦӴ‫ࡃ୿ޢ‬.
[5] ൶එ බ, ᣽‫܇‬щ‫ ܖ‬I (ᙆᓙ৐, 2002).
[6] ޽஭ ѱ, ƠǐƏƱƭᲦᇹ 2 ࠇᇹ 2 ӭ (2005).