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Thus, (12.16) reduces to the form (12.13). In writing down (12.16), we have assumed that the other nucleons in 14 0 are simply spectators to the decaying proton. However, a priori, we cannot ignore the fact the nucleons participating in /3-decay are bound inside nuclei. We also have no reason to believe the idealized form of weak nucleon current, J(Nl, shown in (12.17), since the nucleons themselves are composite objects and not structureless Dirac particles. Despite these problems, it turns out to be quite easy to get an accurate estimate of G. There are several reasons for this. First, the low-energy weak interaction is essentially a point interaction, and we can ignore the longer-range strong interaction effects we just mentioned. Actually, there is a beautiful and more precise justification for this vague argument. The weak current (fp y"1/;,,) and its conjugate (f" y"1/;p)' together with the electromagnetic current (f py"1/; p)' are believed to form an isospin triplet of conserved vector currents. This is referred to as the conserved vector current hypothesis. The intimate connection with the electromagnetic current "protects" the vector part of the weak current from any strong interaction corrections, just as the electromagnetic charge is protected. The axial vector part, fI1Y"y5 yp , will not contribute to the process as we are considering a transition between two JP = 0+ nuclear states,

3 The Pointer wrapper class, as written in Figure 57, requires operator<:thus we cannot use operator> and instantiate the priority-queue with a greater function template

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

which precludes a change of parity. Moreover, since the process occurs between two J = 0 nuclei, we can safely assume that the nuclear wavefunction is essentially unchanged by the transition. Another simplifying feature is that the energy released in the decay (about 2 MeV) is small compared to the rest energy of the nuclei. We can therefore use nonrelativistic spinors for the nucleons [see (6.11)], and then only yl' with 1L = 0 contributes [see (6.13)]. Thus,

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/ / Comparison function for HuffNode / / Meaning is reversed so priority-queue will retrive the min

82.07 0.02276 -0.7783 0.1640

return 1hsweight > rhsweight;

/ / Construct the Huffman coding tree void HuffmanTree::createTree( ) i priority-queue<Pointer<HuffNode>, vector<Pointer<HuffNode> > , less<Pointer<HuffNode> > > pq;

If; =

HuffNode *newNode = new HuffNode( i , theCountsgetCount( i ) , NULL, NULL, NULL theNodes [ i ] = newNode; pqpush( Pointer<HuffNode>( newNode ) 1 ;

theNodes [ END ] = new Huf Node ( END, 1, NULL, NULL, NULL pqpush( Pointer<HuffNode>i theNodes[ END I ) ) ; while( pqsize(

So the estimated regression equation is Y = 82.07 + 0.02276X. - 0.7783X 2 + 0.1640X3 (If you want to verify this, use a computer. Calculation of formula (3.8) using an ordinary hand calculator is feasible for p = 1 but is difficult for p = 3.) A more complete analysis of these data is outlined in Example 1 in Section 2.4. At the beginning of the analysis, model (3.6) is used, but it is found that the following model is better:

[u(Pv)y (1- y5)v(Pe)1!t/;t(x)t[;p(x)e-i(p,+p,jOXd 4 x,

) ) ;

> 1 )

HuffNode *nl = pqtop( ) ; pqpop( ) ; HuffNode *n2 = pqtop( ) ; pqpop( ) ; HuffNode *result = new HuffNode( INCOMPLETE-CODE, nl->weight + n2->weight, nl, n2, NULL nl->parent = n2->parent = result; pqpushi Pointer<HuffNode>( result ) ) ;

(12.18)

root = pqtop (

(3.9)

Pointer<Huf Node> object in order to add it to the priority queue) At lines 24 and 25 we add the end-of-file symbol The loop that extends from lines 27 to 35 is a line-for-line translation of the tree construction algorithm While we have two or more trees, we extract two trees from the priority queue, merge the result, and put it back in the priority queue At the end of the loop, only one tree is left in the priority queue, and we can extract it and set root

where, as remarked after (12.11), the v spinor v( Pe) describes an outgoing positron of momentum Pe' The e+ and p are emitted with an energy of the order of 1 MeV, and so their de Broglie wavelengths are about 10- 11 cm, which is much larger than the nuclear diameter. We can therefore set

The tree produced by createTree is dependent on how the priority queue breaks ties Lnfortunately this means that if the program is compiled on two different machines, with two different STL priority-queue implementations, it is possible to compress a file on the first machine, and then be unable to obtain the original when attempting to uncompress on the second machine Avoiding this problem requires some additional work

.

X4 = The estimated regression equation is 0.03367X] + 5.425X 2 - 0.5026X3 - 0.1209Xi-

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