# Presentation: 666892

## Weak Interactions in the Nucleus II

- Summer School, Tennessee
-  June 2003

## Recoil effects in E&M

**Recoil effects in E&M**

***Recoil effects***

***Has to be zero to allow***
***conservation of charge:***

***Anomalous magnetic moment***

**Hadrons exchange**** gluons **
**so need to include most general **
**Lorentz-invariant terms in**
** ****interaction**

## Recoil effects in Weak decays

***Recoil effects***

**g****S**** and g****WM****: Conservation of the Vector Current: **
***I******=1***** form factors in *****V*****E&M**** ****are identical**** ****to**** form factors in *****V*****WEAK**

**g****PS****: Partial Conservation **
**of the Axial Current**
**(plus pion-pole dominance): **

***g******T*****: Second Class Currents:**
**breaking of G-parity **

## Conservation of the Vector Current: 

***I******=1***** form factors in *****V*****E&M**** ****are identical**** ****to**** form factors in *****V*****WEAK**

**14****O**

**14****C**

**14****N**

***I=1,J************=0******+***

***I=1,J************=0******+***

***I=1,J************=0******+***

***Shape of beta spectrum,***
*********, determines <g******WM******>***
***for WEAK***

***Width of M1 and (e,e’)***
***cross-section***
***determine <g******WM******>***
***for E&M***

- Garcia and B.A. Brown,
- Phys Rev. C 52, 3416 (1995).

***Potential for checking CVC***
***at fraction of % level***

## gPS: Partial Conservation 

**of the Axial Current**
**(plus pion-pole dominance): **

**Measure intensity of *********** + p =************ + n *********

**Approximation should hold very well : *****u***** and *****d *****quarks are very light**
**chiral symmetry: ****V. Bernard et al. *****Phys. Rev. D 50, 6899 (1994).***

**Radiative ******** capture**

**Ordinary ******** capture**

## gT: Second Class Currents:

***g******T*****: Second Class Currents:**
**breaking of G-parity **

***In 1970’s***** evidence that *****(ft)******+******/(ft)******- *****changed linearly with end-point energy**

## Slide 7

## Slide 8

## From R. D. McKeown, et al.Phys. Rev. C 22, 738-749 (1980) 

- From R. D. McKeown, et al.Phys. Rev. C **22**, 738-749 (1980)

## From Minamisono et al.

- Phys. Rev. Lett. 80, 4132(1998).

## Angular momentum and Rotations

**Invariance:**

**Rotating the coordinate system:**

**For any rotation:**

**Invariance under rotations**** imply ****conservation of J **

## Isospin

**Notice *****n+n, n+p, p+p***** hadronic interactions are very similar. **

**Use spin formalism to take into account Pauli exclusion principle etc. **

## Slide 13

## Weak Decays of Quarks

- Once upon a time:

**Weak interactions needed neutral component to render *****g sin************= e.***

_**s**_

**d**

**Z****0**

********

********

**But the process **
**K****L****0************+********-**** **
**could not be observed. **
**Why not??**** **

## Weak Decays of Quarks

**The neutral weak **
**currents go like:**

**No strangeness-changing**
**Neutral Currents**

**G.I.M. proposed**

## Weak Decays of Quarks

**The neutral weak **
**currents go like:**

**The process **
**K****L****0************+********-**** **
**actually goes through **
**this diagram **

**u  c**

****

**G.I.M. proposed**

## Finding J/Psi confirmed the existence of the c quark and 

**Finding J/Psi confirmed the existence of the c quark and **
**gave validity to the G.I.M. hypothesis**

## Weak decays in the Standard Model

**From nuclear**
** ****0.974**

**Ke3  0.220**

- 0.080

- d

- u

- 

- 

- e+

- e+

- e

- e

- W

**CKM matrix: Is it really Unitary?**

**I**

**1/2**

**1/2**

## In order to measure Vud we compare intensities for semi-leptonic to purely leptonic decays

- In order to measure Vud we compare intensities for semi-leptonic to purely leptonic decays

- d

- u

- 

- 

- e+

- e+

- e

- e

- Fermi’s Golden rule:
****-1  α  |<f H i>|2 f(E)
- Then:
***|<f****** I ******i>|******2*** Vud2  f /fquarks

## Example: decay of 14O

***I=1 Iz=1, J************=0******+***

**14****O (t1/2=70.6 s)**

***I=1 Iz=0, J************=0******+***

**14****N**

***branch <1%***

***Additional branches so ***
***small that beta intensity ***
***can almost be obtained***
***directly from ******14******O half-life***

***14******O easy to produce***
***and half-life convenient***
***for separating from other***
***radioactivity.***

***Level density not high***
***so Isospin config. ***
***mixing very small.***

***Many features contribute***
***to allowing a precise***
***determination of ft***

## Nuclear weak decays are driven by two currents : V and AV is conserved (in the same sense that the electromagnetic current is conserved).

- Initially most precise results came from decays for which only *V* can contribute:
-    J(Initial nucleus)=0+  J(Final nucleus)=0+

## From Hardy et al, Nucl. Phys. A509, 429 (1990).

- Note this
- range is
- only 0.5%

**Nuclear 0+ ******** 0+ decays:**

**2.3******** away from 1**

## Complication: Isospin symmetry breaking

**Nuclei do have charge and**

**To understand it we can separate it into effects at two different levels:**

**1) decaying proton and new-born neutron sample different mean fields.**

**2) shell-model configurations are mixed**

**n**

**p**

**E**

## From Hardy et al, Nucl. Phys. A509, 429 (1990).

- Radiative and isospin breaking corrections have to be taken into account.

## The complication of isospin-breaking correctionscan be circumvented by looking at: 1) +0 e+ 2) n  p e- 

******+************0**** e****+**** ********has a very small branch (********10****-8****);**

**2) n ******** p e****-**** ********is a mixed transition ****(*****V********* and *****A*********contribute********.**

## Determinnig Vud from neutron  decay

**Disadvantage**: V and A contribute to this J=1/2+  1/2+ decay. Consequently need to measure 2 quantities with precision.
-  **Advantage**: Simplest nuclear decay. No isospin-breaking corrections.

- Neutron  already well known: need to determine  asymmetry (e- angular distribution) from polarized neutrons.

## Slide 27

## Cold-Neutron Decay

**Cold-Neutron Decay**

## J.C. Hardy, 2003

**J.C. Hardy, 2003**

## Beta asymmetry with beam of Cold Neutrons (v  500 m/s)

**momentum**

**Beta asymmetry with beam of Cold Neutrons (*****v***** ******** 500 m/s)**

**e****-**

**neutron**
**spin**

**vacuum **
**beam pipe**

**B field decreases to**
**decrease transverse**
**component of momentum**
**which lowers backscattering**

**Abele et al. **
**Phys. Rev. Lett. 88, 211801 (2002).**

## Ultra-Cold Neutron Source Layout(LANL)

- Liquid N2

- Be reflector

- Solid D2

- 77 K poly

- Tungsten Target

- 58Ni coated stainless guide

- UCN Detector

- Flapper
- valve

- LHe

- SS UCN Bottle

- Saunders, 2003
- C. Morris et al, PRL 89, 272501

## Line C Measurements

- UCN
- Detector

- Cold Neutron
- Detector

- Proton
- Beam

- Line C results show reduced ( 100) UCN production.
- D2 frost on guide windows and walls.
- Gravity+Aluminum detector window

- Saunders, 2003
- C. Morris et al, PRL 89, 272501

## Solid D2 in a “windowless” container

- Grown from a gas phase at 50 mbar

- Cooled through the triple point

- Saunders, 2003
- C. Morris et al, PRL 89, 272501

## Slide 34

## Neutrons in Magnetic Field

- In a frame rotating with freq. 

## Neutrons in Magnetic Field

- In a frame rotating with freq. 

- Field ***B******1*** rotating
- with freq. 
- around ***B******0 ******.***

***strength of B******0***

***freq. of B******1***

***strength of B******1***

## Neutrons in Magnetic Field

- In S’ motion is precession around ***B******e****** ***with angular velocity ***a = -************B******e***