U.S. Open champion Simpson to skip British Open; Mickelson improves with 64 July 13, 2012 -- Updated 1840 GMT (0240 HKT) Webb Simpson holds his championship trophy after winning the 112th U.S. Open but will not be at the British Open. U.S. Open champion Webb Simpson out of British Open Simpson's wife in due to give birth later this month Phil Mickelson shoots eight-under-par 64 at Scottish Open Alexander Noren and Francesco Molinari joint leaders at Castle Stuart (CNN) -- U.S. Open champion Webb Simpson pulled out this year's British Open Friday because his wife is due to give birth later this month. Simpson was set to fly in next week to the third major of the season at Royal Lytham and St Annes from July 19-22 but has decided against making the trip. A statement issued by tournament organizers said: "Webb Simpson, the 2012 U.S. Open Champion, has withdrawn from The Open Championship due to family reasons." A number of leading contenders have been tuning up for Lytham at this week's Scottish Open and there was a welcome return to form for four-time major champion Phil Mickelson. Mickelson holed his second shot for an eagle two at his opening hole at Castle Stuart and backed it up with six birdies for a second round eight-under 64. The American had opened with a disappointing 73 at the links course in Inverness but on seven-under 137 at halfway is handily placed for a weekend charge. "There was big difference today compared to my 73 yesterday as I just hit a lot better shots, struck it solidly and made a few more putts," he told he official European Tour website. I have only played three tournaments the last couple of months so I knew I just needed to play more, and I'm glad I added this tournament. I have only played three tournaments the last couple of months so I knew I just needed to play more Phil Mickelson Mickelson finished joint runner-up to Darren Clarke at last year's British Open and his last victory came at February's AT&T Pebble Beach National Pro-Am where he finished with a 64. He trails joint leaders Alexander Noren of Sweden and Italian Francesco Molinari by five shots. Molinari had led after the opening round with a superb 62 but came back to the field with second round 70. Defending champion and world number one Luke Donald stayed in contention on nine-under after a 68, seeking his second win in his last three starts on the European Tour.