- Email: [email protected]
Nuclear motion correction to exotic atom level widths
V01ume 468, num6er 3
NUCLEAR
PHY51C5 LE77ER5
M0710N
C0RREC710N
1 0ct06er 1973
70 EX071C
A70M
LEVEL W1D7H5 ~
M. L E 0 N L05 A1am05 5c1ent1f1cLa60rat0ry, L05 A1am05, New Mex1c0 87544, u5A and
R. 5EK1 ca11f0rn1a 5tate un1ver51ty, N0rthr1d9e, ca11f0rn1a 91324, u5A Rece1ved 12 Au9u5t 1973 7he effect 0f nuc1ear m0t10n 0n ex0t1c at0m rad1at10n rate515 d15cu55ed. 7he 1nc1u510n 0f th15 effect 15 e55ent1a1 1f nuc1ear a650rpt10n rate5 are t0 6e der1ved fr0m exper1menta1 X-ray y1e1d5.
A5 p01nted 0ut 50me t1me a90 6y Fr1ed and Mart1n [1], 1n ca1cu1at1n9 the rad1at10n (and Au9er) deexc1tat10n rate5 0f ex0t1c at0m5, 0ne 5h0u1d u5e the center0f-ma55 e1ectr1c d1p01e m0ment. 7h15 exceed5 the nuc1ear-center d1p01e m0ment 6y the fact0r e- 2m +M m+M •
where m 15 the ••me50n•• ma55 and 2 and M the nuc1ear char9e and ma55; hence the rad1at10n (and Au9er) rate5 are enhanced 0ver the 5tat10nary nuc1eu5 va1ue5 6y a fact0r 0f e 2. When the mea5ured X-ray y1e1d5 are u5ed t0 extract the 5tr0n9-1nteract10n a650rpt10n rate5, 1t 15 0f c0ur5e e55ent1a1 t0 1nc1ude th15 fact0r (a5 empha512ed 6y Fr1ed and Mart1n [1]). 7h15 n0t 15 pr0mpted 6y the fact that, 1amenta61y, m05t the0ret1ca1 and exper1menta1 hadr0n1c at0m w0rk [2] 5eem5 n0t t0 1nc1ude th15 fact0r, and 50 1t appear5 that the nuc1ear m0t10n c0rrect10n 15 n0t w1de1y apprec1ated. A5 a re5u1t, ev1dent1y, there ha5 recent1y 6een d15cu55ed a ••d15crepancy•• 6etween the exper1menta1 5tr0n9 1nteract10n w1dth5 0f pa1r5 0 f K- at0m 1eve15 (e.9., 4f and 3d 1eve15 0f K - - 325) and the pred1ct10n5 0f a phen0men01091ca1 10ca1 K--nuc1eu5 0pt1ca1 p0tent1a1 [3]. Here the 10wer 1eve1 w1dth wa5 mea5ured d1rect1y wh11e the upper 0ne wa5 determ1ned fr0m the y1e1d 0f upper ~ 10wer X-ray5.7he ••d15crepancy•• c0n515t5 0f the upper w1dth 6e1n9 t00 5ma11 6y a fact0r 0 f ~ 2 ; when the e 2 fact0r 15 pr0per1y 1nc1uded,
th1515 reduced t0 ~ 2 / 1 . 5 , and, hence, 15 n0 10n9er very 519n1f1Cant. F0r ~ at0m5 the e 2 fact0r 151ar9er ( ~ 2 . 0 ) and, a5 an examp1e, the c0rrect10n5 t0 the 0n1y pU6115hed y1e1d data [4] are 5h0wn 1n ta61e 1. F0r ~;- at0m5 the fact0r 15 ~ 2 . 2 . 7a61e 1 Exper1menta1 ant1pr0t0n1c 5tr0n9 1nteract10n 1eve1w1dth5, 6ef0r and after nuc1ear m0t10n c0rrect10n (data 0f 8acken5t055 et a1. 14]. 7ar9et
7ran51t10n runc0rrected (eV) 1•c0rrected(eV)
P
5~ 4
5
5 --• 4
C1
5~ 4
K
5~ 4
5n
8~ 7
+ 0.90 1.54 • 0.64
3.08 + 1.80 - 1.28
1
8~ 7
+ 3 87 5.00 • 2104
9.95
Pr
8 -+ 7
+ 0.12 -0.09 +0.33 1.43 - 0.24 + 1.07 3.85•0.71 0.55
12.70
12.4
+ 3.34 -2.23
+ 28.5 -
6.8
+ 0.25 -0.19 +0.70 3.05 - 0.51 + 2.20 8.01 • 1.49 1.14
26.80
24.8
+ 7.05 -4.70
+ 7.70 4.06 + 57.0 - 13.6
Reference5
5upp0rted 1n part 6y the U.5. At0m1c Ener9y C0mm15510n and 1n part 6 y the Nat10na1 5c1ence F0undat10n.
[1] 2. Fr1ed and A.D. Mart1n, Nu0v0 c1m. 29 (1963) 574. 299
V01ume 468, num6er 3
PHY51C5 LE77ER5
[2] E.9., J.E. Ru55e11, Phy5. Rev. A1 (1970) 742; W.W. 5app, Jr., M. Eckhan5e, 6.M. M111erand R.E. We15h, Phy5. Rev. C5 (1971) 690; R. 5ek1and R. Kun5e1man, Phy5. Rev. C7 (1973) 1260; C.E. W1e9and, Phy5. Rev. Letter5 22 (1969) 1235; 7.E.0. Er1c50n and F. 5check, Nuc1. Phy5. 819 (1970) 450;
300
1 0ct06er 1973
K. A51am and J.R. R00k, Nuc1. Phy5. 820 (1970) 397; H.A. 8ethe and P.J. 51men5, Nuc1. Phy5. 821 (1970) 589. [3] H. K0ch, F1fth 1ntern. C0nf. 0n H19h ener9y phy51c5 and nuc1ear 5tructure, Upp5a1a, 5weden, 1973. [4] 6.8acken5t055 et a1., Phy5. Letter5 418 (1972) 552.
NUCLEAR
PHY51C5 LE77ER5
M0710N
C0RREC710N
1 0ct06er 1973
70 EX071C
A70M
LEVEL W1D7H5 ~
M. L E 0 N L05 A1am05 5c1ent1f1cLa60rat0ry, L05 A1am05, New Mex1c0 87544, u5A and
R. 5EK1 ca11f0rn1a 5tate un1ver51ty, N0rthr1d9e, ca11f0rn1a 91324, u5A Rece1ved 12 Au9u5t 1973 7he effect 0f nuc1ear m0t10n 0n ex0t1c at0m rad1at10n rate515 d15cu55ed. 7he 1nc1u510n 0f th15 effect 15 e55ent1a1 1f nuc1ear a650rpt10n rate5 are t0 6e der1ved fr0m exper1menta1 X-ray y1e1d5.
A5 p01nted 0ut 50me t1me a90 6y Fr1ed and Mart1n [1], 1n ca1cu1at1n9 the rad1at10n (and Au9er) deexc1tat10n rate5 0f ex0t1c at0m5, 0ne 5h0u1d u5e the center0f-ma55 e1ectr1c d1p01e m0ment. 7h15 exceed5 the nuc1ear-center d1p01e m0ment 6y the fact0r e- 2m +M m+M •
where m 15 the ••me50n•• ma55 and 2 and M the nuc1ear char9e and ma55; hence the rad1at10n (and Au9er) rate5 are enhanced 0ver the 5tat10nary nuc1eu5 va1ue5 6y a fact0r 0f e 2. When the mea5ured X-ray y1e1d5 are u5ed t0 extract the 5tr0n9-1nteract10n a650rpt10n rate5, 1t 15 0f c0ur5e e55ent1a1 t0 1nc1ude th15 fact0r (a5 empha512ed 6y Fr1ed and Mart1n [1]). 7h15 n0t 15 pr0mpted 6y the fact that, 1amenta61y, m05t the0ret1ca1 and exper1menta1 hadr0n1c at0m w0rk [2] 5eem5 n0t t0 1nc1ude th15 fact0r, and 50 1t appear5 that the nuc1ear m0t10n c0rrect10n 15 n0t w1de1y apprec1ated. A5 a re5u1t, ev1dent1y, there ha5 recent1y 6een d15cu55ed a ••d15crepancy•• 6etween the exper1menta1 5tr0n9 1nteract10n w1dth5 0f pa1r5 0 f K- at0m 1eve15 (e.9., 4f and 3d 1eve15 0f K - - 325) and the pred1ct10n5 0f a phen0men01091ca1 10ca1 K--nuc1eu5 0pt1ca1 p0tent1a1 [3]. Here the 10wer 1eve1 w1dth wa5 mea5ured d1rect1y wh11e the upper 0ne wa5 determ1ned fr0m the y1e1d 0f upper ~ 10wer X-ray5.7he ••d15crepancy•• c0n515t5 0f the upper w1dth 6e1n9 t00 5ma11 6y a fact0r 0 f ~ 2 ; when the e 2 fact0r 15 pr0per1y 1nc1uded,
th1515 reduced t0 ~ 2 / 1 . 5 , and, hence, 15 n0 10n9er very 519n1f1Cant. F0r ~ at0m5 the e 2 fact0r 151ar9er ( ~ 2 . 0 ) and, a5 an examp1e, the c0rrect10n5 t0 the 0n1y pU6115hed y1e1d data [4] are 5h0wn 1n ta61e 1. F0r ~;- at0m5 the fact0r 15 ~ 2 . 2 . 7a61e 1 Exper1menta1 ant1pr0t0n1c 5tr0n9 1nteract10n 1eve1w1dth5, 6ef0r and after nuc1ear m0t10n c0rrect10n (data 0f 8acken5t055 et a1. 14]. 7ar9et
7ran51t10n runc0rrected (eV) 1•c0rrected(eV)
P
5~ 4
5
5 --• 4
C1
5~ 4
K
5~ 4
5n
8~ 7
+ 0.90 1.54 • 0.64
3.08 + 1.80 - 1.28
1
8~ 7
+ 3 87 5.00 • 2104
9.95
Pr
8 -+ 7
+ 0.12 -0.09 +0.33 1.43 - 0.24 + 1.07 3.85•0.71 0.55
12.70
12.4
+ 3.34 -2.23
+ 28.5 -
6.8
+ 0.25 -0.19 +0.70 3.05 - 0.51 + 2.20 8.01 • 1.49 1.14
26.80
24.8
+ 7.05 -4.70
+ 7.70 4.06 + 57.0 - 13.6
Reference5
5upp0rted 1n part 6y the U.5. At0m1c Ener9y C0mm15510n and 1n part 6 y the Nat10na1 5c1ence F0undat10n.
[1] 2. Fr1ed and A.D. Mart1n, Nu0v0 c1m. 29 (1963) 574. 299
V01ume 468, num6er 3
PHY51C5 LE77ER5
[2] E.9., J.E. Ru55e11, Phy5. Rev. A1 (1970) 742; W.W. 5app, Jr., M. Eckhan5e, 6.M. M111erand R.E. We15h, Phy5. Rev. C5 (1971) 690; R. 5ek1and R. Kun5e1man, Phy5. Rev. C7 (1973) 1260; C.E. W1e9and, Phy5. Rev. Letter5 22 (1969) 1235; 7.E.0. Er1c50n and F. 5check, Nuc1. Phy5. 819 (1970) 450;
300
1 0ct06er 1973
K. A51am and J.R. R00k, Nuc1. Phy5. 820 (1970) 397; H.A. 8ethe and P.J. 51men5, Nuc1. Phy5. 821 (1970) 589. [3] H. K0ch, F1fth 1ntern. C0nf. 0n H19h ener9y phy51c5 and nuc1ear 5tructure, Upp5a1a, 5weden, 1973. [4] 6.8acken5t055 et a1., Phy5. Letter5 418 (1972) 552.