' )2( : 1. )1371( 2. )2671(

, . . . , , . . . - .

- . , = re ) Z = .( 2

e Z2

, 2 n

me M n - - me + M n . L = n , 1 4 Z 2e = , E 22 2 n 1 4 1 2 2 Z 2 e 1 1 1 = , n-) m (n>m 2 2 2 2 R 3 hc m n m n R . )1= m, 2= m, 3= m ...(. . , ) ( ) (He II . , , . ) ,(He I . - , " . 1 1 : ) E 2 .( E 2 n ) n n ,l (

n .l , . :

, . . ) = . H 2

2

,fine structure ( : ) 2 + Veff ( r

1

, ) , , , (. " . 3 ) (. , , , n* n n ,l .

. - ,l . , - ,l , ) (. . - , . , '. . - L S . L S Lz ,Sz . n, l , s ) lz , sz Lz- Sz (

J = L + S j , jz J = L + 2 L S + S , J z . , - n, - n - , j ,J 1+ 2S L S ,L+S 1+ 2S . , . , . )-( 0 J , , )-(, 1 ) ( J 3 -3 . , ) (, . , , ) ( . , , . , , 1 = . L 0 = ) J = 0, 1 , s 0 = J(, . , , , , ), '( - - n . , . . ,

2

2

2

2

. " ) ( . : )(Natural broadening . , . ' . . " , . : 2A w + 0y ( ) = y 2 4 ( 0 )2 + w , ) Collision broadening or Pressure (broadening " . ) .(Doppler broadening ) (. , . . : . f = f 0 v ": cy ( ) = Ae

2) 0( 2 2

+C

" : " . - ) ( - . " , . " . " . " ) ( . ) ( " . " .

3

. SPEX 1680B Double Spectrometer ) .(Photomultiplier ) ( " Origin . :

" 45o . . ) ( . , . ) (. , . : . 0. ) (. " . , .

4

-3 : . " ) ( " , . , . ) (. . " . " . . , . , , . . ) LASER - Light Amplification by Stimulated ,(Emission of Radiation : ) (, . . , . . .

5

' , .

] . 0.0 [ mm , . scanme Origin ) (. ) , . ] 0.02 [ nm , (. , - , . . ] 0.0 [ mm . " - ] ) 0.1, 0.2, 0.3, 0.5 [ mm ( - ] . 632.8 [ nm - ] 0.1[ mm ] . 0.1, 0.2 [ mm , " ) (. " - Curve Fitting Tool ,Matlab : 2A w + 0) y ( ) = y w , - A 2 4 ( 0 )2 + w . y ( ) = Ae

2) 0( 2 2

0 ,( y = y : + C

) (: ) , ) max 0.1, w ( 0 , 2 ( - ) ) max ( 0.1, ( .

(

)

, - Curve Fitting Tool 0 ] 0.1[ nm ) , ] , 0.02 [ nm (. ' ), '( ' , ) A1e (. ' 6

2) 10( 21 2

+ A2 e

2) 20( 22 2

+C

, ) ( "" .

' - - , . )5002.5.22, 5.42 -5.52(.

, , ] . 632.8 [ nm . ) - ] .( 400 [ nm ] < < 700 [ nm ) ( -.logbook )/( 0 0 . 0 , theory - 0) (. : , . , ) ( - = ) - N' (. 1 N , - 0 - 0 + - 0 -

) (

.

) 0(

2

+

)) ( (

2

- ] ) 0.02 [ nm ( . , ( ) = a + b - 1 a, b. - 0 - 0 + a 0 + b - 0 -

.

( (1 + a ) ) + ( 2 0

0

) a ) + ( b2

2

- , ) " ( ) (. . , - 1 fitpoly- Matlab " 2.R

7

) "" (. , , , - " " " ". , , , , . "" , . , , , . ' - )5.22( ) ( .

, - ..., . H , H , , . ) (, )/( ) (. , , , . " 1 1 1 . 2 > , = R 2 2 n n 2 n 1 1 1 1 1 2 . = a 2 + b 2 , n n : " R = a a " . R = 4b 4b 2 1- . R = 10973731.6 m ' - )5.22, 5.42( , .

. .

= < 3 .

x X

) ( x ) + ( X2

2

2 " : x x- X X , - 1 < .

8

, , , - . 1 n1 L 2 n2 L ) ( . 1 = R n 1 1 n1L

(

1

) (n2

1 2 n2 L

2

)

2

" , , , , + 2 1 , )( 2 1 2 1 = ) 2 2 2 1 , " (. : ) ( 3p-6d ] 466 [ nm] 498 [ nm ] 569 [ nm ] 589 [ nm ] 616 [ nm

3p-5d 3p-4d 3s-3p 3p-5s

1 1 , , = R 2 2 n 2n2 n2 L 1 1 n1L 3 s , 5 s , 3 p , 4 d , 5 d , 6 d )

1

(

( )

)

(. 110.0 = 4 d = 6 d ) ( 4 d = 6 d solve .Matlab = AnL 1

) ( n nL

2

1

A3 s , A5 s , A3 p , A4 d , A5 d , A6 d

1

= R An1L1 An2 L2

(

2

)2

= , A6 d " 7 -7 , . nL = n " "

) ( 6 4d

= , A4 d

1

) ( 4 4d

1 : AnL

9

, nL + = n

1 AnL+

) i + = i + i ( + AnL = . nL

nL + nL2

i = i i .

' - )5.52( .

) (. ) m ( m p + mn me m p ,( e . - ) > me + ( m p + mn ) me + m p - , D - : H 4 2 2 Z 2 e , - R h 3c , )(.

D 4272000.1 = H

, - ..., ) H , H (. ' ) (, , . , " ) - '(, ) ( , , . 1 1 ', ) ( 2 n 4 2 2 Z 2 e . R h 3c 2 2 R D = D . D = D RD + RH H RH H H RD RH . .

y ( ) = Ae

2) 0( 2 2

, + C

.

Ae

2) 0( 2 2

) ( d = 2 A

01

AD , AH , D , H " AD D = . D AD D + AH H ) .( ( D2

) D ' ,

' - )5.52( . )( - .

. . : )( )(. 2 R, , ) (. ' - )5.52( .

] , 400 [ nm ] < < 700 [ nm, , 50nm ] 0.1[ mm . , , ) - (, . find Matlab 1.0 , , ) (. , .

11

' , 0.0mm . :Intensity with both slits set on 0.0mm 70.0 60.0 50.0 40.0 Intensity 30.0 20.0 10.0 0 10.0- 20.0- 726

826

926

036

136

236

336

436

][nm

" : 0.0mm 0.1mm :Intensity as function of wavelength in He-Ne laser Data points Gaussian fit Lorentzian fit

006

005

004 Intensity

003

002

001

0 726 826 926 036 136 236 336 436

][nm

119.0=2 ,R 569.0=2R

.

21

0.1mm 0.1mm :Intensity as function of wavelength in He-Ne laser 007 Data points Lorentzian fit Gaussian fit

006

005

Intensity

004

003

002

001

0 726 826 926 036 136 236 336 436

][nm

559.0=2 ,R 209.0=2R

, . 0.2mm :0.1mmIntensity as function of wavelength in He-Ne laser Data points Lorentzian fit Gaussian fit

006

005

004 Intensity

003

002

001

0 726 826 926 036 136 236 336 436

][nm

859.0=2 ,R 168.0=2R

, , ) , (.

31

-) 0.1mm ,(0.0mm , ) 0.3mm :(0.0mm)Intensity as function of wavelength in He-Ne laser (saturation 006

005

004 Intensity

003

002

001

0 726

826

926

036

136

236

336

436

][nm

, , , , . . : 0.0mm - 0.1mm ) (. , , , ) , (.

41

' 50.50.22 : 2ex [nm] [nm] th [nm] [nm] Gauss R2 Lorentz R 8.236 135901.0 2.236 6.0 569.0 119.0 69.675 478690.0 8.675 61.0 839.0 429.0 60.645 328780.0 9.545 61.0 199.0 359.0 5.194 7190.0 16.194 11.0 879.0 559.0 4.534 3880.0 48.534 44.0 199.0 659.0 2.404 260.0 66.404 64.0 299.0 379.0 .=0.320.20nm

2ex [nm] [nm] th [nm] [nm] Gauss R 7.236 401.0 8.236 1.0 3469.0 3.404 66.404 560.0 63.0 3989.0 6.534 38.534 660.0 32.0 9289.0 8.545 70.645 560.0 72.0 399.0 8.675 69.675 801.0 61.0 7989.0System callibration on may 24th 6.0 )72.086.0(+y=(-0.00090.0005)x 5.0 83.0=R2=0.72 2/freedom

50.50.42 :

:

4.0

] [nm

3.0

2.0

1.0

0

1.0- 004

054

005

055

006

056

] [nm

2 R , .

51

50.50.52 :]ex [nm] [nm] th [nm] [nm Gauss 2R 5769.0 889.0 5969.0 769.0 499.0 4099.0

5.236 1.404 4.534 6.545 6.675 6.096

770.0 560.0 280.0 680.0 380.0 790.0

8.236 66.404 38.534 70.645 69.675 57.096

3.0 65.0 34.0 74.0 63.0 51.0

:System callibration on may 25th 7.0 )22.020.1(+y=(-0.00120.0004)x 6.0 374.0=R2=0.816 2/freedom

5.0

] [nm

4.0

3.0

2.0

1.0

0 004

054

005

055 ] [nm

006

056

007

, ) ( . -0.626,7.426= ) ( ' - ) ( ) (: ] [nm transition ]1-y=-1 [m-1] y [m 21/n ][nm 96.556 2 3 = 0.22362 n 21.025 600+1.5251e 11111.0 H 80.584 2 4 = 0.22361 n 92.059 600+2.0615e 5260.0 H 81.334 2 5 = 0.25612 n 9.4631 600+2.3085e 40.0 H H ) ( 2 R , -2.0, .

61

:

) (. 7 : 01 6100.0 4201.1 = . RH m , 41.3 = .

RH : %51.0 = RH

7 : 01 6000.0 0001.1 = . RH m

, 83.4 = .

RH : %50.0 = RH

71

' - , 498nm :

. . - . :

, .

81

) ( ) -50.42(: Transition ]calibrated [nm ]effective [nm ] [nm 79.664 3p-6d 77.664 2.0 75.664 43.894 3p-5d 41.894 3.0 49.794 89.865 3p-4d 86.865 3.0 83.865 61.985 3s-3p 64.985 3.0 67.985 41.616 3p-5s 48.516 3.0 45.516 , solve ,Matlab 4 . . ) , (: Level theory (0.0005) calculated

3s 5s 3p 4d 5d 6d

373.1 253.1 288.0 110.0 310.0 110.0

9273.1 0253.1 0388.0 9110.0 5110.0 9110.0

7000.0 5100.0 9000.0 4100.0 0200.0 4100.0

%50.0 %11.0 %1.0 %8.11 %4.71 %8.11

21.0 0 79.0 16.0 37.0 16.0

' - , ) - ( :HIntensity as function of wavelength 61 41 21 01 y t i s n e t n I 8 6 4 2 0 584 Data Double Gaussian fit Gaussian (single) fit

9.584 8.584 7.584 6.584 5.584 4.584 3.584 2.584 1.584 ][nm

91

, . 2R )539.0 999.0 (. : ] [nm transition ]1-y=-1 [m-1] y [m 21/n ][nm 3.8751 600+2.3036e 1.434 2 3 = 0.29742 n 11111.0 H 40.684 2 4 = 0.31001 n 3.2131 600+2.0575e 5260.0 H 32.656 2 5 = 0.35669 n 82.828 600+1.5238e 40.0 H : ] [nm transition ]1-y=-1 [m-1] y [m 21/n ][nm 434 2 3 = 0.29739 n 9.8751 600+2.3041e 11111.0 H 49.584 2 4 = 0.30998 n 7.2131 600+2.0579e 5260.0 H 30.656 2 5 = 0.35663 n 56.828 600+1.5243e 40.0 H :

02

: 1291200.0 5649690.1 = RH : 99291200.0 5879690.1 = . RH . :

D : 728200.0 920000.1 = H D D H 90.0 = . %82.0 = . 272000.1 = D H theory H . :

H H H

D 895.0 165.0 096.0.

D

D

: 70.0 26.0 = . D : %77.01 =

12

' - ) - ( . , (cftool) Matlab 0 x . :

. ) ( :] [nm ] [nm 2R 47.204 72092.0 56498.0 32.214 37303.0 4688.0 25.414 55003.0 1427.0 98.834 82803.0 35779.0 81.744 9903.0 6699.0 54.174 17903.0 6699.0 33.294 95113.0 97499.0 26.785 99633.0 35399.0 28.766 21063.0 4799.0 ) ( . , -) 471nm (

22

- ) 471.44579nm, 471.46945nm, 471.44748nm , (. ' - -, -.500nm :

-].500[nm2 [nm] [nm] Intensity R 51992.0 94.144 6069.0 3823.0 22992.0 97.144 6069.0 6142.0 75503.0 61.864 28.88 9299.0 61503.0 64.664 321.1 9299.0 65803.0 42.084 9.191 5399.0 38513.0 19.805 6.592 1499.0 16713.0 8.515 5.1 1499.0 53343.0 91.016 2571.0 88.0 61843.0 79.626 2704.0 979.0 68943.0 68.236 4808.0 979.0 10053.0 63.336 7581.0 979.0 51353.0 51.446 1.271 3099.0 36553.0 46.256 35.02 1499.0 41553.0 49.056 147.2 1499.0

:

32

186 96.396 99.396 88.696

50463.0 78763.0 69763.0 38863.0

13.32 78.43 76.42 462.0

2299.0 6499.0 6499.0 6499.0

" - : theory measured 8549.764 61.864 417.0 4521.084 42.084 73.0 0427.805 19.805 95.0 9420.446 51.446 53.0 ) , (, .

42

' - , . - ) ( - . , . . ) ( ) ( . ' - . : "" , ) ( . , . . , . " . , . , . ' , ) , ) 1 2 .( 1 1 2 ( R n n . . - ) (. H )5 , (. ' , , , . , . ,

52

. , ) ( . " , . ' . . -1 01 , . ) 0.1nm (. , . , , )91.0= -%2.0 (. )50.52( " . )%11 ( . , - ,H , , ) 2 R (. . , , . , , . ' , . . - ) ( . , . ' , . - 652.64nm . , . . , , .

62

Broadening: 1. Saleh,Bahaa E.A, Teich Malvin Carl B./Fundamentals of Photonics,ch.12.2 D. 2. http://hyperphysics.phy-astr.gsu.edu/hbase/atomic/broaden.html 3. http://www.thespectroscopynet.com/Theory/Lineshape.asp Quantum Defect Theory: 4. Condon and Shortley / Theory of Atomic Spectra, p. 141-147 5. http://www.shef.ac.uk/physics/teaching/phy332/atomic_physics4.pdf Experimental equipment: 6. http://www.tau.ac.il/~lab3/SPECTROSCOPY/monochromator2.pdf 7. http://www.chem.vt.edu/chem-ed/optics/detector/pmt.html Spectral lines: 8. http://physics.nist.gov/PhysRefData/ASD/lines_form.html

27

. , . 50.50.22 )(mm 0.0 0.0 1.0 1.0 2.0 2.0 )(mm 1.0 1.0 1.0 1.0 1.0 1.0 )0 (nm )/w (nm A 0y 2R

2.236 9122.0 9.822 119.0 579.6- 2.236 5901.0 5.726 -569.0 2.236 7264.0 6.784 559.0 57.31 2.236 932.0 6.336 -209.0 1.236 769.0 4.196 859.0 99.23 1.236 426.0 4.065 -168.0 .

) , ( 2 2 )0 (nm) (nm) R (Gauss) R (Lorentz

8.675 9.545 5.194 4.534 2.404

9690.0 8780.0 7190.0 3880.0 260.0950.0

839.0

429.0

9.875

4990.0

839.0

429.0

199.0 5879.0 8099.0 299.0299.0

8259.0 5559.0 6559.0 379.0379.0

3.704

)0 (nm) (nm) R (Gauss) R (Lorentz 70.0 7499.0 7369.0 0.656 H 70.0 9839.0 2509.0 4.584 H 61.0 8591.0 6171.0 5.334 H H . )0 (nm 4.885 985 3.914 4.814 2.024 ) (nm) R2 (Gauss) R2 (Lorentz 5180.0 5299.0 1259.0 7570.0 5299.0 1259.0 5561.0 3459.0 9839.0 701.0 3459.0 9839.0 3390.0 3459.0 9839.0

2

2

82

5.524 8.624 1.624 7.224 6.924 5.134 7.234 434 8.534

4821.0 6031.0 5611.0 3521.0 9741.0 931.0 3661.0 7902.0 801.0

5759.0 5759.0 5759.0 5759.0 5759.0 6529.0 6529.0 8179.0 8179.0

5118.0 5118.0 50.50.42

Up Down

7.236

]0 [nm

] [nm

R Gauss

2

R Lorentz

2

7301.0

3469.0

3519.0

4.236

3909.0 2279.0 429.0 .2 2

)0 (nm

) (nm

)R (Gauss) R (Lorentz

3.404 6.534

96460.029160.0

3989.03989.0

7059.07059.0

4.704 5.434

5560.093970.0

9289.09289.0

639.0639.0

8.545 8.6758.875

50560.0 801.04701.0

399.0 7989.07989.0

759.0 4659.04659.0

)0 (nm 8.054 5.944 254 2.554 7.664 3.664 1.574 6.474 4.374 6.674 1.894 7.794 3.515 9.415

) (nm 6121.0 7942.0 6531.0 4311.0 8321.0 4021.0 3151.0 9851.0 7851.0 8203.0 6621.0 4231.0 3231.0 5421.0

)R (Gauss) R (Lorentz 3759.0 8229.0 3759.0 8229.0 3759.0 8229.0 599.0 1959.0 8879.0 5259.0 8879.0 5259.0 8539.0 3749.0 8539.0 3749.0 8539.0 3749.0 8539.0 3749.0 7799.0 4189.0 7799.0 4189.0 4099.0 4469.0 4099.0 4469.0

2

2

92

2.615 8.865 2.865 985 6.985 616 4.516 7.766 2.666 4.576 7.286 8.186

9321.0 3021.0 5021.0 6741.0 7541.0 51960.0 2370.0 7241.0 6022.0 2121.0 8611.0 78670.0

4099.0 2799.0 2799.0 6889.0 6889.0 2599.0 2599.0 8779.0 8779.0 3199.0 7158.0 7158.0

4469.0 7769.0 7769.0 7959.0 7959.0 879.0 879.0 7439.0 7439.0 3479.0 3418.0 3418.0 50.50.52

Up Down]0 [nm 1.404 2.704 5.334 3.434 4.534 6.545 6.675 6.875 9.975 0.626 7.426 0.326 6.096

]0 [nm 5.236 2.236 ] [nm 8460.0 7360.0 70.0 570.0 280.0 4680.0 380.0 580.0 940.0 380.0 6770.0 650.0 700.0

] [nm 770.0 580.0 R Gauss 889.0 889.0 5969.0 5969.0 5969.0 769.0 7399.0 7399.0 7399.0 9499.0 9499.0 9499.0 4099.02

R2 Gauss 5769.0 359.0 R Lorentz 349.0 349.0 2229.0 2229.0 2229.0 229.0 279.0 279.0 279.0 1869.0 1869.0 1869.0 9189.02

R2 Lorentz 5219.0 998.0

H H H

]0 [nm ] [nm A 60.53 37.48 56270.0 58440.0 0.656 8.556 9.556 87680.0 79.86 737.6 5.41 35760.0 32040.0 6.584 5.584 6.584 15170.0 41 719.1 320.5 88670.0 64560.0 6.334 5.334 5.334 12180.0 197.5

R 4799.0 5878.0 999.0 7439.0 45899.0 34299.0

2

03

0 [nm] 402.2 411.7 414.0 438.4 446.7 471.0 491.9 501.2 587.3 667.6 0 [nm] 441.0 441.3 467.7 466.0 479.8 508.5 515.4 609.9 626.7 632.6 633.1 643.9 652.4 650.7 680.8 693.5 693.8 696.7

[nm] 0.07486 0.1295 0.1206 0.1262 0.1255 0.1098 0.06935 0.06944 0.07984 0.07298 [nm] 0.06536 0.06555 0.06782 0.07171 0.06627 0.0725 0.06624 0.09043 0.06879 0.07161 0.0734 0.0671 0.06963 0.06392 0.07162 0.07302 0.07043 0.06282 A 0.3283 0.2416 88.82 1.123 191.9 295.6 1.5 0.1752 0.4072 0.8084 0.1857 172.1 20.53 2.741 23.31 34.87 24.67 0.2636

R (Gauss) 0.89465 0.8864 0.7241 0.97753 0.9984 0.9966 0.9949 0.9948 0.9935 0.9974 R2 0.9606 0.9606 0.993 0.993 0.9935 0.9941 0.9941 0.88 0.979 0.979 0.979 0.9903 0.994 0.994 0.9921 0.9946 0.9946 0.9946

2

31