2. rutherford backscattering spectrometry basic principles

Download 2. RUTHERFORD BACKSCATTERING SPECTROMETRY Basic Principles

Post on 05-Jan-2016

219 views

Category:

Documents

1 download

Embed Size (px)

TRANSCRIPT

  • 2. RUTHERFORDBACKSCATTERINGSPECTROMETRYBasic Principles

  • ELASTIC COULOMB SCATTERINGConsider an ion of charge z, mass m and initial kinetic energy Eo being scattered elastically from a stationary nucleus of charge Z and mass M purely by the Coulomb force. The final energy E of the scattered ion is a function of the angle of scatter from the initial direction and the ratio M/m. m, Eom, EM, 0M, (Eo E)Recoiling nucleusScattered ion

  • KINEMATIC FACTORThe scattered E can be derived from the principles of conservation of energy and momentum, and is given by (in laboratory frame of reference):

    The multiplication factor k on the right hand side of the equation is often referred to as the kinematic factor. For M/m > 1, k is a slow-varying function of , having the maximum value of 1 at = 0 and the minimum value at = 180o. For M/m = 1, the value of k is zero beyond 90o.

  • M/m = 1M/m = 4M/m = 20Plots of k vs for M/m = 0, 4, 20

    Chart1

    111

    0.96984636080.99242910260.9984819026

    0.88302241110.97024221740.9939869776

    0.7500003830.93495464590.9866897931

    0.58682466960.88889450680.9768698698

    0.41317663710.83493908020.9648957215

    0.2500007660.7762052980.9512047015

    0.11697844180.7157420510.9362804818

    0.0301540930.65626965980.9206300589

    00.60000041110.904762025

    00.54855573460.8891674898

    00.50297514480.874304575

    00.46379537040.8605868866

    00.43116962820.8483758945

    00.40499779030.8379767554

    00.38504567290.8296368511

    00.37104153740.8235461802

    00.36274639880.8198387371

    00.360.8185941043

    q

    k

    Sheet1

    14201

    angleE1E2E3

    01.001.001.00

    100.970.991.00

    200.880.970.99

    300.750.930.99

    400.590.890.98

    500.410.830.96

    600.250.780.95

    700.120.720.94

    800.030.660.92

    900.000.600.90

    1000.000.550.89

    1100.000.500.87

    1200.000.460.86

    1300.000.430.85

    1400.000.400.84

    1500.000.390.83

    1600.000.370.82

    1700.000.360.82

    1800.000.360.82

    M/menergy

    10.00

    50.44

    100.67

    150.77

    200.82

    250.85

    300.88

    350.89

    400.90

    450.91

    500.92

    550.93

    600.94

    650.94

    700.94

    750.95

    800.95

    850.95

    900.96

    950.96

    1000.96

    Sheet1

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Sheet2

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Sheet3

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    q

    k

  • Plots of k vs M/m for = 180oThe small gradient at large M/m ratios implies that mass separation is poor for higher M/m ratios.

    Chart2

    0

    0.4444444444

    0.6694214876

    0.765625

    0.8185941043

    0.8520710059

    0.8751300728

    0.8919753086

    0.9048185604

    0.9149338374

    0.9231064975

    0.9298469388

    0.9355012094

    0.940312213

    0.9444554652

    0.9480609418

    0.9512269471

    0.954029205

    0.9565269895

    0.9587673611

    0.960788158

    M/m

    k

    Sheet1

    14201

    angleE1E2E3

    01.001.001.00

    100.970.991.00

    200.880.970.99

    300.750.930.99

    400.590.890.98

    500.410.830.96

    600.250.780.95

    700.120.720.94

    800.030.660.92

    900.000.600.90

    1000.000.550.89

    1100.000.500.87

    1200.000.460.86

    1300.000.430.85

    1400.000.400.84

    1500.000.390.83

    1600.000.370.82

    1700.000.360.82

    1800.000.360.82

    M/menergy

    10.00

    50.44

    100.67

    150.77

    200.82

    250.85

    300.88

    350.89

    400.90

    450.91

    500.92

    550.93

    600.94

    650.94

    700.94

    750.95

    800.95

    850.95

    900.96

    950.96

    1000.96

    Sheet1

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Sheet2

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    M/m

    k

    Sheet3

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    q

    k

  • DIFFERENTIAL SCATTERING CROSS SECTIONThe theoretical differential cross section for a given scattering angle is given by:

    The higher order terms are usually negligible for M>m and the differential cross section can be expressed in the following form, which has the unit of mb/sr (millibarns per steradian) when MeV is used as the unit for Eo:

  • ds/d versus qThe dependence of ds/d on sin-4(q/2) means that ds/d has very large values at small forward scattered angles and approaches infinity at 0o. However, for q = 90o to 180o, it decreases rather slowly because sin-4(q/2) drops gradually from a value of 4 at 90o to 1 at 180o. The diagram below shows the plots of ds/d vs q for the Coulomb scattering of 2 MeV 4He+ ions for oxygen and calcium.Ca (Z=20, A=40)O (Z=8, A=16)

    Chart2

    359367.9002199652246062.98437478

    22803.2187742154142533.725338846

    4618.466809535928879.0255595992

    1512.78137638219468.491602388

    647.43787883144060.0947426965

    329.18501659742071.014353734

    188.99280394031194.813024627

    118.8744161849756.5731011557

    80.3522200998515.8093756237

    57.6237628227373.7565176419

    43.4620568532285.2458553327

    34.2720753035227.808470647

    28.1422708673189.4971929207

    24.0019207917163.6200049481

    21.2284733005146.2859581281

    19.4534774789135.192234243

    18.4626618392128.999636495

    18.1440000001127.0080000005

    qo

    ds/dW (mb/sr)

    Sheet1

    14201

    angleE1E2E3

    01.001.001.00

    100.970.991.00

    200.880.970.99

    300.750.930.99

    400.590.890.98

    500.410.830.96

    600.250.780.95

    700.120.720.94

    800.030.660.92

    900.000.600.90

    1000.000.550.89

    1100.000.500.87

    1200.000.460.86

    1300.000.430.85

    1400.000.400.84

    1500.000.390.83

    1600.000.370.82

    1700.000.360.82

    1800.000.360.82

    M/mk

    10.00

    50.44

    100.67

    150.77

    200.82

    250.85

    300.88

    350.89

    400.90

    450.91

    500.92

    550.93

    600.94

    650.94

    700.94

    750.95

    800.95

    850.95

    900.96

    950.96

    1000.96

    Sheet1

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Sheet2

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    M/m

    k

    Sheet3

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    q

    k

    820

    0.250.1

    qx-sectionx-section

    103593682246063

    2022803142534

    30461828879

    4015139468

    506474060

    603292071

    701891195

    80119757

    9080516

    10058374

    11043285

    12034228

    13028189

    14024164

    15021146

    16019135

    17018129

    18018127

    Ex-section

    0.17258

    0.21814

    0.3806

    0.4454

    0.5290

    0.6202

    0.7148

    0.8113

    0.990

    1.073

    1.160

    1.250

    1.343

    1.437

    1.532

    1.628

    1.725

    1.822

    1.920

    2.018

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    qo

    ds/dW (mb/sr)

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    E (MeV)

    ds/dW(mb/sr)

  • ds/d versus Eods/d is inversely proportional to the square of the incident ion energy Eo, implying that it increases with decreasing Eo. This also means that for a thick target, more ions are scattered from a greater depth. The diagram below show a plot of ds/d vs Eo for the scattering of 4He+ from an aluminium target at q = 180o.Projectile: 4He+Target: AlScatter angle: 180o

    Chart4

    20942.8996608

    5235.7249152

    2326.9888512

    1308.9312288

    837.715986432

    581.7472128

    427.4061155265

    327.2328072

    258.5543168

    209.428996608

    173.0818153785

    145.4368032

    123.9224832

    106.8515288816

    93.079554048

    81.8082018

    72.4667808332

    64.6385792

    58.0135724676

    52.357249152

    E (MeV)

    ds/dW(mb/sr)

    Sheet1

    14201

    angleE1E2E3

    01.001.001.00

    100.970.991.00

    200.880.970.99

    300.750.930.99

    400.590.890.98

    500.410.830.96

    600.250.780.95

    700.120.720.94

    800.030.660.92

    900.000.600.90

    1000.000.550.89

    1100.000.500.87

    1200.000.460.86

    1300.000.430.85

    1400.000.400.84

    1500.000.390.83

    1600.000.370.82

    1700.

Recommended

View more >