By Haroon Asghar, 1,a) Raheel Ali, 1 and M. Aslam Baig 2,b)

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23a) (26 b ) t h e marginal exact in ( R , . R2) o f We n o t e r e a l , ^ . lim conditions ( 2 6 a ) m F i g . , 2=1 , = corresponds We -a ,_dlnN__x-1 ^ d r ^ curve which i b , b dInQ d r I^ { ^ ) ^ ^ ^ m the λ = J^^Ti evaluation of a ,^'Γ^~7Γ7Γ~7'~~ -1)(S^+S2) + Numerical (25) under equations i b ) f 2 cosh g ^ ^ j Setting "~ΤΒΓ e + ^ t h e exactly ' ' P ^ x )- T. |Γ(| find obtains. obtains Ji b tanh A s t a b i l i t y t o a r e , with t h e same E q . (18b): - n) ( 2 7 ) 58 From (23 bute to a,b) the l o c a l i z e d are in it is easily dispersion the seen relation region ji/2 that trapped only if the 3 J I / 2 < x< electrons contri eigenfunction where these is electrons trapped.

V) a r e dfined with where f a c t o r , t o V)^^ ( h ^ ) . E q . ( 5 ) lowest (V,X,^) I t is s u r f a c e d λ, «>^ρ(Λ) ΐ ο ( ΐ ) ( \ ) ' and d l n N / d Y A 0 is a "slow" P o i s s o n ' s function equation o f X(13Ln0/3\ ) « | m I ) . In f i r s t reads (8) where = ^il^m^^e ^ b roughly t h e bounce frequency 1/2 Β o m 3Λ,m 52 i. 1/2 ' ñ Eq. (4a) lb). ed is The and readily solution solved which untrapped in the vanishes particles framework at the of our boundary model ( E q . between trapp- is G) e , m F ^ e"^^^° dX — e F^«/2 1/2 Here we a s s u m e d V^j(I) have + " » g i ' (9) 1) A f t e r performing 4^6 BdMdid:5 Z^/H'i)^^'^ = V^j the ^-il^^o μ and integration set one V^.

In E q . -0 tional t o ^ i k " is obviously similar t o t h e linear term and ax therefore represents t h e e f f e c t o f nonlinear diamagnetic d r i f t s . 64 The term proportional to 9Φ°. 9 X corresponds to nonlinear E^xB d r i f t s . /Τ^. where 2 c^. 2 / Ω ^ lating 2 , 9/95 as exp λ,^ = _ - S'''e . , V^{\) t ~ 0 ω,^. (-iωj^t) dlnN = e"^Ji ^ o ^ ^ k ^ ' ~ Γο (λ|,) , * k^^ ~k2 -37-· φ is ^j^g e l e c t r o s t a t i c ^i^ = ~ p o t e n t i a l , o s c i l with (11) (12) 65 L a s t l y (13a) 4 , k " , k , k " = I'' where k^ Zj^ = prohibited Hence the linear and ν^^/Ω^· for We note ^ / 2 / of E q .

### Determination of transition probabilities for the 3p fi 3s transition array in neon using laser induced breakdown spectroscopy by Haroon Asghar, 1,a) Raheel Ali, 1 and M. Aslam Baig 2,b)

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